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vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Садржај</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">помери на страну</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">сакриј</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Почетак</div> </a> </li> <li id="toc-Definicija" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definicija"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Definicija</span> </div> </a> <ul id="toc-Definicija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Motivišuća_svojstva" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Motivišuća_svojstva"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Motivišuća svojstva</span> </div> </a> <button aria-controls="toc-Motivišuća_svojstva-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Садржај одељка Motivišuća svojstva</span> </button> <ul id="toc-Motivišuća_svojstva-sublist" class="vector-toc-list"> <li id="toc-Dodatna_svojstva" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dodatna_svojstva"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Dodatna svojstva</span> </div> </a> <ul id="toc-Dodatna_svojstva-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Kontrast_sa_medijanom" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kontrast_sa_medijanom"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Kontrast sa medijanom</span> </div> </a> <ul id="toc-Kontrast_sa_medijanom-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Generalizacije" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Generalizacije"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Generalizacije</span> </div> </a> <button aria-controls="toc-Generalizacije-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Садржај одељка Generalizacije</span> </button> <ul id="toc-Generalizacije-sublist" class="vector-toc-list"> <li id="toc-Ponderisana_aritmetička_sredina" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ponderisana_aritmetička_sredina"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Ponderisana aritmetička sredina</span> </div> </a> <ul id="toc-Ponderisana_aritmetička_sredina-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kontinuirane_raspodele_verovatnoće" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kontinuirane_raspodele_verovatnoće"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Kontinuirane raspodele verovatnoće</span> </div> </a> <ul id="toc-Kontinuirane_raspodele_verovatnoće-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Uglovi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Uglovi"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Uglovi</span> </div> </a> <ul id="toc-Uglovi-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Simboli_i_kodiranje" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Simboli_i_kodiranje"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Simboli i kodiranje</span> </div> </a> <ul id="toc-Simboli_i_kodiranje-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Primena" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Primena"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Primena</span> </div> </a> <ul id="toc-Primena-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Primeri" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Primeri"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Primeri</span> </div> </a> <button aria-controls="toc-Primeri-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Садржај одељка Primeri</span> </button> <ul id="toc-Primeri-sublist" class="vector-toc-list"> <li id="toc-Primer_1" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Primer_1"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Primer 1</span> </div> </a> <ul id="toc-Primer_1-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Primer_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Primer_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Primer 2</span> </div> </a> <ul id="toc-Primer_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Vidi_još" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vidi_još"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Vidi još</span> </div> </a> <ul id="toc-Vidi_još-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reference" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reference"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Reference</span> </div> </a> <ul id="toc-Reference-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Literatura" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Literatura"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Literatura</span> </div> </a> <ul id="toc-Literatura-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spoljašnje_veze" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Spoljašnje_veze"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Spoljašnje veze</span> </div> </a> <ul id="toc-Spoljašnje_veze-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Садржај" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Садржај" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Прикажи/сакриј садржај" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Прикажи/сакриј садржај</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Aritmetička sredina</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Чланак на другим језицима. Доступан на: 63" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-63" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">63 језика</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AA%D9%88%D8%B3%D8%B7_%D8%AD%D8%B3%D8%A7%D8%A8%D9%8A" title="متوسط حسابي — арапски" lang="ar" hreflang="ar" data-title="متوسط حسابي" data-language-autonym="العربية" data-language-local-name="арапски" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Media_aritm%C3%A9tica" title="Media aritmética — астуријски" lang="ast" hreflang="ast" data-title="Media aritmética" data-language-autonym="Asturianu" data-language-local-name="астуријски" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C6%8Fd%C9%99di_orta" title="Ədədi orta — азербејџански" lang="az" hreflang="az" data-title="Ədədi orta" data-language-autonym="Azərbaycanca" data-language-local-name="азербејџански" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Rata-rata_aritmetika" title="Rata-rata aritmetika — индонежански" lang="id" hreflang="id" data-title="Rata-rata aritmetika" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонежански" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Min_aritmetik" title="Min aritmetik — малајски" lang="ms" hreflang="ms" data-title="Min aritmetik" data-language-autonym="Bahasa Melayu" data-language-local-name="малајски" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D0%B0%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D1%87%D0%BD%D0%B0_%D1%81%D1%82%D0%BE%D0%B9%D0%BD%D0%BE%D1%81%D1%82" title="Средноаритметична стойност — бугарски" lang="bg" hreflang="bg" data-title="Средноаритметична стойност" data-language-autonym="Български" data-language-local-name="бугарски" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%8F%D1%80%D1%8D%D0%B4%D0%BD%D1%8F%D0%B5_%D0%B0%D1%80%D1%8B%D1%84%D0%BC%D0%B5%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D0%B5" title="Сярэдняе арыфметычнае — белоруски" lang="be" hreflang="be" data-title="Сярэдняе арыфметычнае" data-language-autonym="Беларуская" data-language-local-name="белоруски" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Aritmeti%C4%8Dka_sredina" title="Aritmetička sredina — босански" lang="bs" hreflang="bs" data-title="Aritmetička sredina" data-language-autonym="Bosanski" data-language-local-name="босански" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Mitjana_aritm%C3%A8tica" title="Mitjana aritmètica — каталонски" lang="ca" hreflang="ca" data-title="Mitjana aritmètica" data-language-autonym="Català" data-language-local-name="каталонски" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%C4%83%D0%BB%D0%BB%D0%B0_%D0%B2%C4%83%D1%82%D0%B0%D0%BC%D0%BC%D0%B8" title="Арифметикăлла вăтамми — чувашки" lang="cv" hreflang="cv" data-title="Арифметикăлла вăтамми" data-language-autonym="Чӑвашла" data-language-local-name="чувашки" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Aritmetick%C3%BD_pr%C5%AFm%C4%9Br" title="Aritmetický průměr — чешки" lang="cs" hreflang="cs" data-title="Aritmetický průměr" data-language-autonym="Čeština" data-language-local-name="чешки" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Arithmetisches_Mittel" title="Arithmetisches Mittel — немачки" lang="de" hreflang="de" data-title="Arithmetisches Mittel" data-language-autonym="Deutsch" data-language-local-name="немачки" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Aritmeetiline_keskmine" title="Aritmeetiline keskmine — естонски" lang="et" hreflang="et" data-title="Aritmeetiline keskmine" data-language-autonym="Eesti" data-language-local-name="естонски" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Arithmetic_mean" title="Arithmetic mean — енглески" lang="en" hreflang="en" data-title="Arithmetic mean" data-language-autonym="English" data-language-local-name="енглески" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Media_aritm%C3%A9tica" title="Media aritmética — шпански" lang="es" hreflang="es" data-title="Media aritmética" data-language-autonym="Español" data-language-local-name="шпански" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Aritmetika_meznombro" title="Aritmetika meznombro — есперанто" lang="eo" hreflang="eo" data-title="Aritmetika meznombro" data-language-autonym="Esperanto" data-language-local-name="есперанто" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Batezbesteko_aritmetiko_sinple" title="Batezbesteko aritmetiko sinple — баскијски" lang="eu" hreflang="eu" data-title="Batezbesteko aritmetiko sinple" data-language-autonym="Euskara" data-language-local-name="баскијски" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%DB%8C%D8%A7%D9%86%DA%AF%DB%8C%D9%86_%D8%AD%D8%B3%D8%A7%D8%A8%DB%8C" title="میانگین حسابی — персијски" lang="fa" hreflang="fa" data-title="میانگین حسابی" data-language-autonym="فارسی" data-language-local-name="персијски" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Moyenne_arithm%C3%A9tique" title="Moyenne arithmétique — француски" lang="fr" hreflang="fr" data-title="Moyenne arithmétique" data-language-autonym="Français" data-language-local-name="француски" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Me%C3%A1n_uimhr%C3%ADocht%C3%BAil" title="Meán uimhríochtúil — ирски" lang="ga" hreflang="ga" data-title="Meán uimhríochtúil" data-language-autonym="Gaeilge" data-language-local-name="ирски" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Media_aritm%C3%A9tica" title="Media aritmética — галицијски" lang="gl" hreflang="gl" data-title="Media aritmética" data-language-autonym="Galego" data-language-local-name="галицијски" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%9E%D7%95%D7%A6%D7%A2_%D7%97%D7%A9%D7%91%D7%95%D7%A0%D7%99" title="ממוצע חשבוני — хебрејски" lang="he" hreflang="he" data-title="ממוצע חשבוני" data-language-autonym="עברית" data-language-local-name="хебрејски" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%AE%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%A4%E0%A4%B0_%E0%A4%AE%E0%A4%BE%E0%A4%A7%E0%A5%8D%E0%A4%AF" title="समान्तर माध्य — хинди" lang="hi" hreflang="hi" data-title="समान्तर माध्य" data-language-autonym="हिन्दी" data-language-local-name="хинди" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Aritmeti%C4%8Dka_sredina" title="Aritmetička sredina — хрватски" lang="hr" hreflang="hr" data-title="Aritmetička sredina" data-language-autonym="Hrvatski" data-language-local-name="хрватски" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%AB%D5%BB%D5%AB%D5%B6_%D5%A9%D5%BE%D5%A1%D5%A2%D5%A1%D5%B6%D5%A1%D5%AF%D5%A1%D5%B6" title="Միջին թվաբանական — јерменски" lang="hy" hreflang="hy" data-title="Միջին թվաբանական" data-language-autonym="Հայերեն" data-language-local-name="јерменски" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Media_aritmetica" title="Media aritmetica — италијански" lang="it" hreflang="it" data-title="Media aritmetica" data-language-autonym="Italiano" data-language-local-name="италијански" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%AE%97%E8%A1%93%E5%B9%B3%E5%9D%87" title="算術平均 — јапански" lang="ja" hreflang="ja" data-title="算術平均" data-language-autonym="日本語" data-language-local-name="јапански" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D0%BE%D1%80%D1%82%D0%B0_%D1%88%D0%B0%D0%BC%D0%B0" title="Арифметикалық орта шама — казашки" lang="kk" hreflang="kk" data-title="Арифметикалық орта шама" data-language-autonym="Қазақша" data-language-local-name="казашки" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D0%BA_%D0%BE%D1%80%D1%82%D0%BE_%D1%81%D0%B0%D0%BD" title="Арифметикалык орто сан — киргиски" lang="ky" hreflang="ky" data-title="Арифметикалык орто сан" data-language-autonym="Кыргызча" data-language-local-name="киргиски" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%98%E1%9E%92%E1%9F%92%E1%9E%99%E1%9E%98%E1%9E%93%E1%9E%96%E1%9F%92%E1%9E%9C%E1%9E%93%E1%9F%92%E1%9E%92" title="មធ្យមនព្វន្ធ — кмерски" lang="km" hreflang="km" data-title="មធ្យមនព្វន្ធ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="кмерски" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%82%B0%EC%88%A0_%ED%8F%89%EA%B7%A0" title="산술 평균 — корејски" lang="ko" hreflang="ko" data-title="산술 평균" data-language-autonym="한국어" data-language-local-name="корејски" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Valor_medius_arithmeticus" title="Valor medius arithmeticus — латински" lang="la" hreflang="la" data-title="Valor medius arithmeticus" data-language-autonym="Latina" data-language-local-name="латински" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Aritm%C4%93tiskais_vid%C4%93jais" title="Aritmētiskais vidējais — летонски" lang="lv" hreflang="lv" data-title="Aritmētiskais vidējais" data-language-autonym="Latviešu" data-language-local-name="летонски" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Aritmetinis_vidurkis" title="Aritmetinis vidurkis — литвански" lang="lt" hreflang="lt" data-title="Aritmetinis vidurkis" data-language-autonym="Lietuvių" data-language-local-name="литвански" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Sz%C3%A1mtani_k%C3%B6z%C3%A9p" title="Számtani közép — мађарски" lang="hu" hreflang="hu" data-title="Számtani közép" data-language-autonym="Magyar" data-language-local-name="мађарски" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D1%87%D0%BA%D0%B0_%D1%81%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D0%B0" title="Аритметичка средина — македонски" lang="mk" hreflang="mk" data-title="Аритметичка средина" data-language-autonym="Македонски" data-language-local-name="македонски" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Rekenkundig_gemiddelde" title="Rekenkundig gemiddelde — холандски" lang="nl" hreflang="nl" data-title="Rekenkundig gemiddelde" data-language-autonym="Nederlands" data-language-local-name="холандски" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Aritmetisk_gjennomsnitt" title="Aritmetisk gjennomsnitt — норвешки букмол" lang="nb" hreflang="nb" data-title="Aritmetisk gjennomsnitt" data-language-autonym="Norsk bokmål" data-language-local-name="норвешки букмол" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Aritmetisk_middeltal" title="Aritmetisk middeltal — норвешки нинорск" lang="nn" hreflang="nn" data-title="Aritmetisk middeltal" data-language-autonym="Norsk nynorsk" data-language-local-name="норвешки нинорск" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/O%CA%BBrta_arifmetik" title="Oʻrta arifmetik — узбечки" lang="uz" hreflang="uz" data-title="Oʻrta arifmetik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="узбечки" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Media_aritm%C3%A9tica" title="Media aritmética — Piedmontese" lang="pms" hreflang="pms" data-title="Media aritmética" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/%C5%9Arednia_arytmetyczna" title="Średnia arytmetyczna — пољски" lang="pl" hreflang="pl" data-title="Średnia arytmetyczna" data-language-autonym="Polski" data-language-local-name="пољски" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/M%C3%A9dia_aritm%C3%A9tica" title="Média aritmética — португалски" lang="pt" hreflang="pt" data-title="Média aritmética" data-language-autonym="Português" data-language-local-name="португалски" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Medie_aritmetic%C4%83" title="Medie aritmetică — румунски" lang="ro" hreflang="ro" data-title="Medie aritmetică" data-language-autonym="Română" data-language-local-name="румунски" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D1%80%D0%B5%D0%B4%D0%BD%D0%B5%D0%B5_%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5" title="Среднее арифметическое — руски" lang="ru" hreflang="ru" data-title="Среднее арифметическое" data-language-autonym="Русский" data-language-local-name="руски" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8%D9%8A_%D8%B3%D8%B1%D8%A7%D8%B3%D8%B1%D9%8A" title="حسابي سراسري — синди" lang="sd" hreflang="sd" data-title="حسابي سراسري" data-language-autonym="سنڌي" data-language-local-name="синди" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Mesi_aritmetik" title="Mesi aritmetik — албански" lang="sq" hreflang="sq" data-title="Mesi aritmetik" data-language-autonym="Shqip" data-language-local-name="албански" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%83%E0%B6%B8%E0%B7%8F%E0%B6%B1%E0%B7%8A%E0%B6%AD%E0%B6%BB_%E0%B6%B8%E0%B6%B0%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B6%B1%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B6%BA" title="සමාන්තර මධ්‍යන්‍යය — синхалешки" lang="si" hreflang="si" data-title="සමාන්තර මධ්‍යන්‍යය" data-language-autonym="සිංහල" data-language-local-name="синхалешки" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Aritmetick%C3%BD_priemer" title="Aritmetický priemer — словачки" lang="sk" hreflang="sk" data-title="Aritmetický priemer" data-language-autonym="Slovenčina" data-language-local-name="словачки" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Aritmeti%C4%8Dna_sredina" title="Aritmetična sredina — словеначки" lang="sl" hreflang="sl" data-title="Aritmetična sredina" data-language-autonym="Slovenščina" data-language-local-name="словеначки" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%86%D8%A7%D9%88%DB%95%D9%86%D8%AF%DB%8C_%DA%98%D9%85%DB%8E%D8%B1%DB%95%DB%8C%DB%8C" title="ناوەندی ژمێرەیی — централни курдски" lang="ckb" hreflang="ckb" data-title="ناوەندی ژمێرەیی" data-language-autonym="کوردی" data-language-local-name="централни курдски" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Aritmeti%C4%8Dka_sredina" title="Aritmetička sredina — српскохрватски" lang="sh" hreflang="sh" data-title="Aritmetička sredina" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="српскохрватски" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Arithmetic_mean" title="Arithmetic mean — сундски" lang="su" hreflang="su" data-title="Arithmetic mean" data-language-autonym="Sunda" data-language-local-name="сундски" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Aritmeettinen_keskiarvo" title="Aritmeettinen keskiarvo — фински" lang="fi" hreflang="fi" data-title="Aritmeettinen keskiarvo" data-language-autonym="Suomi" data-language-local-name="фински" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Aritmetiskt_medelv%C3%A4rde" title="Aritmetiskt medelvärde — шведски" lang="sv" hreflang="sv" data-title="Aritmetiskt medelvärde" data-language-autonym="Svenska" data-language-local-name="шведски" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A1%E0%B8%B1%E0%B8%8A%E0%B8%8C%E0%B8%B4%E0%B8%A1%E0%B9%80%E0%B8%A5%E0%B8%82%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95" title="มัชฌิมเลขคณิต — тајски" lang="th" hreflang="th" data-title="มัชฌิมเลขคณิต" data-language-autonym="ไทย" data-language-local-name="тајски" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Trung_b%C3%ACnh_c%E1%BB%99ng" title="Trung bình cộng — вијетнамски" lang="vi" hreflang="vi" data-title="Trung bình cộng" data-language-autonym="Tiếng Việt" data-language-local-name="вијетнамски" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Aritmetik_ortalama" title="Aritmetik ortalama — турски" lang="tr" hreflang="tr" data-title="Aritmetik ortalama" data-language-autonym="Türkçe" data-language-local-name="турски" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D0%B5%D1%80%D0%B5%D0%B4%D0%BD%D1%94_%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D1%87%D0%BD%D0%B5" title="Середнє арифметичне — украјински" lang="uk" hreflang="uk" data-title="Середнє арифметичне" data-language-autonym="Українська" data-language-local-name="украјински" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8%D8%A7%D8%AA%DB%8C_%D8%A7%D9%88%D8%B3%D8%B7" title="حساباتی اوسط — урду" lang="ur" hreflang="ur" data-title="حساباتی اوسط" data-language-autonym="اردو" data-language-local-name="урду" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%AE%97%E6%9C%AF%E5%B9%B3%E5%9D%87%E6%95%B0" title="算术平均数 — ву кинески" lang="wuu" hreflang="wuu" data-title="算术平均数" data-language-autonym="吴语" data-language-local-name="ву кинески" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%AE%97%E6%9C%AF%E5%B9%B3%E5%9D%87%E6%95%B0" title="算术平均数 — кинески" lang="zh" hreflang="zh" data-title="算术平均数" data-language-autonym="中文" data-language-local-name="кинески" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%AE%97%E8%A1%93%E5%B9%B3%E5%9D%87%E5%80%BC" title="算術平均值 — кантонски" lang="yue" hreflang="yue" data-title="算術平均值" data-language-autonym="粵語" data-language-local-name="кантонски" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q19033#sitelinks-wikipedia" title="Уреди међујезичке везе" class="wbc-editpage">Уреди везе</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Именски простори"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Aritmeti%C4%8Dka_sredina" title="Прочитајте овај чланак [c]" accesskey="c"><span>Чланак</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/%D0%A0%D0%B0%D0%B7%D0%B3%D0%BE%D0%B2%D0%BE%D1%80:Aritmeti%C4%8Dka_sredina" rel="discussion" title="Разговарајте о страници [t]" 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id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Више опција" > <div class="vector-menu-heading"> Радње </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Aritmeti%C4%8Dka_sredina"><span>Читај</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit" title="Уредите ову страницу [v]" accesskey="v"><span>Уреди</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit" title="Уредите изворни код ове странице [e]" accesskey="e"><span>Уреди извор</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=history"><span>Историја</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Опште </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0_%D0%B2%D0%BE%D0%B4%D0%B8_%D0%BE%D0%B2%D0%B0%D0%BC%D0%BE/Aritmeti%C4%8Dka_sredina" title="Списак свих вики страница које воде овамо [j]" accesskey="j"><span>Шта води овамо</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%9F%D0%BE%D0%B2%D0%B5%D0%B7%D0%B0%D0%BD%D0%B5_%D0%B8%D0%B7%D0%BC%D0%B5%D0%BD%D0%B5/Aritmeti%C4%8Dka_sredina" rel="nofollow" title="Скорашње измене страница које су повезане с овом [k]" accesskey="k"><span>Повезане измене</span></a></li><li id="t-upload" class="mw-list-item"><a href="//sr.wikipedia.org/wiki/Википедија:Водич_за_отпремање" title="Поставите слике и снимке [u]" accesskey="u"><span>Отпреми датотеку</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&oldid=28949483" title="Трајна веза до ове измене на овој страници"><span>Трајна веза</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=info" title="Више информација о овој страници"><span>Подаци о страници</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A6%D0%B8%D1%82%D0%B8%D1%80%D0%B0%D1%98&page=Aritmeti%C4%8Dka_sredina&id=28949483&wpFormIdentifier=titleform" title="Информације о томе како цитирати ову страницу"><span>Цитирај страницу</span></a></li><li id="t-urlshortener" class="mw-list-item"><a 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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">помери на страну</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">сакриј</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">С Википедије, слободне енциклопедије</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sr" dir="ltr"><p><b>Aritmetička sredina</b> ili <b>prosek</b> je <a href="/wiki/%D0%9F%D0%BE%D1%98%D0%B0%D0%BC" title="Појам">pojam</a> iz <a href="/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика">statistike</a>. Ona se računa za <a href="/wiki/%D0%A1%D0%BA%D1%83%D0%BF" title="Скуп">skup</a> brojeva kao količnik <a href="/wiki/%D0%97%D0%B1%D0%B8%D1%80" class="mw-redirect" title="Збир">zbira</a> članova i broja članova skupa. U matematičkoj notaciji aritmetička sredina je: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x={x_{1}+\cdots +x_{n} \over n}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mi>n</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x={x_{1}+\cdots +x_{n} \over n}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edffad4e05dd8ca643fd61f4059b9663a72d6a2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.247ex; height:5.009ex;" alt="{\displaystyle x={x_{1}+\cdots +x_{n} \over n}.}" /></span><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Kolekcija je često skup rezultata <a href="/wiki/Experiment" class="mw-redirect" title="Experiment">eksperimenta</a> ili <a href="/w/index.php?title=Observational_study&action=edit&redlink=1" class="new" title="Observational study (страница не постоји)">opservacione studije</a>, ili često skup rezultata iz <a href="/wiki/Survey_(statistics)" class="mw-redirect" title="Survey (statistics)">ankete</a>. Termin „aritmetička sredina“ je poželjniji u nekim kontekstima u matematici i statistici, jer pomaže da se razlikuje od drugih <a href="/w/index.php?title=Average&action=edit&redlink=1" class="new" title="Average (страница не постоји)">proseka</a>, kao što su <a href="/wiki/Geometric_mean" class="mw-redirect" title="Geometric mean">geometrijska sredina</a><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> i <a href="/wiki/Harmonic_mean" class="mw-redirect" title="Harmonic mean">harmonska sredina</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Pored matematike i statistike, aritmetička sredina se često koristi u mnogim različitim oblastima kao što su <a href="/wiki/Economics" class="mw-redirect" title="Economics">ekonomija</a>, <a href="/wiki/Anthropology" class="mw-redirect" title="Anthropology">antropologija</a> i <a href="/wiki/%D0%98%D1%81%D1%82%D0%BE%D1%80%D0%B8%D1%98%D0%B0" title="Историја">istorija</a>, a u izvesnoj meri se koristi u skoro svim akademskim oblastima. Na primer, <a href="/w/index.php?title=Per_capita_income&action=edit&redlink=1" class="new" title="Per capita income (страница не постоји)">dohodak po glavi stanovnika</a> je aritmetički prosečan prihod stanovništva jedne nacije. </p><p>Iako se aritmetička sredina često koristi za izveštavanje o <a href="/wiki/Central_tendency" class="mw-redirect" title="Central tendency">centralnim tendencijama</a>, ona nije <a href="/w/index.php?title=Robust_statistic&action=edit&redlink=1" class="new" title="Robust statistic (страница не постоји)">robusna statistika</a>, što znači da na nju u velikoj meri utiču <a href="/w/index.php?title=Outlier&action=edit&redlink=1" class="new" title="Outlier (страница не постоји)">eksterne</a> vrednosti (vrednosti koje su mnogo veće ili manje od većine vrednosti). Za <a href="/w/index.php?title=Skewed_distribution&action=edit&redlink=1" class="new" title="Skewed distribution (страница не постоји)">iskrivljene raspodele</a>, kao što je <a href="/w/index.php?title=Distribution_of_income&action=edit&redlink=1" class="new" title="Distribution of income (страница не постоји)">raspodela prihoda</a> za koju su prihodi nekoliko ljudi znatno veći od prihoda većine ljudi, aritmetička sredina se možda neće poklapati sa nečijim pojmom „sredine“, a robusna statistika, kao što je <a href="/wiki/%D0%9C%D0%B5%D0%B4%D0%B8%D1%98%D0%B0%D0%BD%D0%B0" class="mw-disambig" title="Медијана">medijana</a>, može dati bolji opis centralne tendencije. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definicija">Definicija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=1" title="Уредите одељак „Definicija”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=1" title="Уреди извор одељка: Definicija"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Za dati <a href="/wiki/Data_set" class="mw-redirect" title="Data set">skup podataka</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X=\{x_{1},\ldots ,x_{n}\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> <mo>=</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X=\{x_{1},\ldots ,x_{n}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c09e28c409c45c4ee539208dc40e404f3c111724" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.514ex; height:2.843ex;" alt="{\displaystyle X=\{x_{1},\ldots ,x_{n}\}}" /></span>, <b>aritmetička sredina</b> (ili <i>srednja vrednost</i> ili <i>prosek</i>), označena kao <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/466e03e1c9533b4dab1b9949dad393883f385d80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:2.009ex;" alt="{\displaystyle {\bar {x}}}" /></span> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /></span> nadvučeno), je srednja vrednost <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" /></span> vrednosti <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{1},x_{2},\ldots ,x_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{1},x_{2},\ldots ,x_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8694289524164f895d6665f163e14c4dc5ec648d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.528ex; height:2.009ex;" alt="{\displaystyle x_{1},x_{2},\ldots ,x_{n}}" /></span>.<sup id="cite_ref-JM_6-0" class="reference"><a href="#cite_note-JM-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Aritmetička sredina je najčešće korišćena i lako razumljiva mera centralne tendencije u skupu podataka. U statistici, pojam <a href="/w/index.php?title=Average&action=edit&redlink=1" class="new" title="Average (страница не постоји)">prosek</a> se odnosi na bilo koju od mera centralne tendencije. Aritmetička sredina skupa posmatranih podataka definisana je kao jednaka zbiru numeričkih vrednosti svakog posmatranja, podeljenog sa ukupnim brojem posmatranja. Simbolički, za skup podataka koji se sastoji od vrednosti <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{1},a_{2},\ldots ,a_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{1},a_{2},\ldots ,a_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e7dfb41e027e24804c6acd07429ef1158f29b60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.229ex; height:2.009ex;" alt="{\displaystyle a_{1},a_{2},\ldots ,a_{n}}" /></span>, aritmetička sredina <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" /></span> je definisana formulom: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\frac {1}{n}}\sum _{i=1}^{n}a_{i}={\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mi>n</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {1}{n}}\sum _{i=1}^{n}a_{i}={\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90330653b40adf032ea8e144f84d7eec1a88054d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:35.426ex; height:6.843ex;" alt="{\displaystyle A={\frac {1}{n}}\sum _{i=1}^{n}a_{i}={\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}}" /></span><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></dd></dl> <p>(za objašnjenje <a href="/w/index.php?title=Summation_operator&action=edit&redlink=1" class="new" title="Summation operator (страница не постоји)">operatora sumiranja</a>, pogledajte <a href="/wiki/Summation" class="mw-redirect" title="Summation">sumiranje</a>.) </p><p>Na primer, uzmite u obzir mesečnu platu 10 zaposlenih u firmi: 2500, 2700, 2400, 2300, 2550, 2650, 2750, 2450, 2600, 2400. Aritmetička sredina je </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {2500+2700+2400+2300+2550+2650+2750+2450+2600+2400}{10}}=2530.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2500</mn> <mo>+</mo> <mn>2700</mn> <mo>+</mo> <mn>2400</mn> <mo>+</mo> <mn>2300</mn> <mo>+</mo> <mn>2550</mn> <mo>+</mo> <mn>2650</mn> <mo>+</mo> <mn>2750</mn> <mo>+</mo> <mn>2450</mn> <mo>+</mo> <mn>2600</mn> <mo>+</mo> <mn>2400</mn> </mrow> <mn>10</mn> </mfrac> </mrow> <mo>=</mo> <mn>2530.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {2500+2700+2400+2300+2550+2650+2750+2450+2600+2400}{10}}=2530.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/011f2bc6eee24c97e784cc28aa7d9581ca564ee9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:81.293ex; height:5.176ex;" alt="{\displaystyle {\frac {2500+2700+2400+2300+2550+2650+2750+2450+2600+2400}{10}}=2530.}" /></span></dd></dl> <p>Ako je skup podataka <a href="/wiki/Statistical_population" class="mw-redirect" title="Statistical population">statistička populacija</a> (tj. sastoji se od svakog mogućeg posmatranja, a ne samo od njihovog podskupa), onda se srednja vrednost te populacije naziva <i><a href="/wiki/Population_mean" class="mw-redirect" title="Population mean">srednja vrednost populacije</a></i> i označava <a href="/wiki/Greek_alphabet" class="mw-redirect" title="Greek alphabet">grčkim slovom</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }" /></span>. Ako je skup podataka <a href="/wiki/Sampling_(statistics)" class="mw-redirect" title="Sampling (statistics)">statistički uzorak</a> (podskup populacije), onda se statistika vrednost koja je rezultat ovog proračuna naziva <i><a href="/w/index.php?title=Sample_mean&action=edit&redlink=1" class="new" title="Sample mean (страница не постоји)">srednjom vrednošću uzorka</a></i> (koja je za skup podataka <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}" /></span> označena kao <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overline {X}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {X}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08fd87d3502c4f9e1b02ac74644474258aeea176" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.131ex; height:3.009ex;" alt="{\displaystyle {\overline {X}}}" /></span>). </p><p>Aritmetička sredina se može na sličan način definisati za <a href="/w/index.php?title=Vector_(mathematics_and_physics)&action=edit&redlink=1" class="new" title="Vector (mathematics and physics) (страница не постоји)">vektore</a> u više dimenzija, ne samo za <a href="/wiki/Scalar_(mathematics)" class="mw-redirect" title="Scalar (mathematics)">skalarne</a> vrednosti; ovo se često naziva <a href="/w/index.php?title=Centroid&action=edit&redlink=1" class="new" title="Centroid (страница не постоји)">centroid</a>. Uopštenije, pošto je aritmetička sredina <a href="/w/index.php?title=Convex_combination&action=edit&redlink=1" class="new" title="Convex combination (страница не постоји)">konveksna kombinacija</a> (zbir koeficijenata je 1), može se definisati na <a href="/wiki/Convex_space" class="mw-redirect" title="Convex space">konveksnom prostoru</a>, a ne samo na vektorskom prostoru. </p> <div class="mw-heading mw-heading2"><h2 id="Motivišuća_svojstva"><span id="Motivi.C5.A1u.C4.87a_svojstva"></span>Motivišuća svojstva</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=2" title="Уредите одељак „Motivišuća svojstva”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=2" title="Уреди извор одељка: Motivišuća svojstva"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Aritmetička sredina ima nekoliko svojstava koja je čine korisnim, posebno kao mera centralne tendencije. Ovim su obuhvaćeni: </p> <ul><li>Ako brojevi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{1},\dotsc ,x_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{1},\dotsc ,x_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/043a9851e76aa50d9939db2bcdd6718c3c325743" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.11ex; height:2.009ex;" alt="{\displaystyle x_{1},\dotsc ,x_{n}}" /></span> imaju srednju vrednost <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/466e03e1c9533b4dab1b9949dad393883f385d80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:2.009ex;" alt="{\displaystyle {\bar {x}}}" /></span>, onda <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x_{1}-{\bar {x}})+\dotsb +(x_{n}-{\bar {x}})=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{1}-{\bar {x}})+\dotsb +(x_{n}-{\bar {x}})=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61d69b253792bdac3317059f25acae0997efd33e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:29.556ex; height:2.843ex;" alt="{\displaystyle (x_{1}-{\bar {x}})+\dotsb +(x_{n}-{\bar {x}})=0}" /></span>. Pošto je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{i}-{\bar {x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{i}-{\bar {x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bd4b83eb042edcf9d6b5507a20b18271682a057" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.299ex; height:2.343ex;" alt="{\displaystyle x_{i}-{\bar {x}}}" /></span> rastojanje od datog broja do srednje vrednosti, u jednom smeru tumačenje ove osobine znači da su brojevi levo od srednje vrednosti uravnoteženi brojevima desno od srednje vrednosti. Srednja vrednost je jedini pojedinačni broj za koji se <a href="/w/index.php?title=Errors_and_residuals_in_statistics&action=edit&redlink=1" class="new" title="Errors and residuals in statistics (страница не постоји)">ostaci</a> (odstupanja od procene) zbrajaju na nulu.</li> <li>Ako se zahteva da se koristi jedan broj kao „tipična“ vrednost za skup poznatih brojeva <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{1},\dotsc ,x_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{1},\dotsc ,x_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/043a9851e76aa50d9939db2bcdd6718c3c325743" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.11ex; height:2.009ex;" alt="{\displaystyle x_{1},\dotsc ,x_{n}}" /></span>, onda aritmetička sredina brojeva to najbolje čini, u smislu minimiziranja zbira kvadrata odstupanja od tipične vrednosti: zbir od <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x_{i}-{\bar {x}})^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{i}-{\bar {x}})^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0774da93861931721c359addb1462c2fbe99117" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.163ex; height:3.176ex;" alt="{\displaystyle (x_{i}-{\bar {x}})^{2}}" /></span>. (Sledi da je srednja vrednost uzorka takođe najbolji pojedinačni prediktor u smislu da ima najmanju <a href="/w/index.php?title=Root_mean_squared_error&action=edit&redlink=1" class="new" title="Root mean squared error (страница не постоји)">srednju kvadratnu grešku</a>.)<sup id="cite_ref-JM_6-1" class="reference"><a href="#cite_note-JM-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Ako se želi aritmetička sredina populacije brojeva, onda je njena procena koja je <a href="/w/index.php?title=Unbiased_estimate&action=edit&redlink=1" class="new" title="Unbiased estimate (страница не постоји)">nepristrasna</a>, aritmetička sredina uzorka uzetog iz populacije.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Dodatna_svojstva">Dodatna svojstva</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=3" title="Уредите одељак „Dodatna svojstva”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=3" title="Уреди извор одељка: Dodatna svojstva"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Avg(c*a_{1},c*a_{2}...c*a_{n})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>v</mi> <mi>g</mi> <mo stretchy="false">(</mo> <mi>c</mi> <mo>∗</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>c</mi> <mo>∗</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mi>c</mi> <mo>∗</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Avg(c*a_{1},c*a_{2}...c*a_{n})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9af8a6fb9260fcd9aa9df4353e4962083c01d1e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.553ex; height:2.843ex;" alt="{\displaystyle Avg(c*a_{1},c*a_{2}...c*a_{n})}" /></span> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c*Avg(a_{1},a_{2}...a_{n})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>∗</mo> <mi>A</mi> <mi>v</mi> <mi>g</mi> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c*Avg(a_{1},a_{2}...a_{n})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55273228250c4cf53e446faf4614c27a1cb849ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.15ex; height:2.843ex;" alt="{\displaystyle c*Avg(a_{1},a_{2}...a_{n})}" /></span></li> <li>Aritmetička sredina bilo kojeg broja grupa brojeva jednake veličine zajedno je aritmetička sredina aritmetičke sredine svake grupe.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Kontrast_sa_medijanom">Kontrast sa medijanom</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=4" title="Уредите одељак „Kontrast sa medijanom”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=4" title="Уреди извор одељка: Kontrast sa medijanom"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r24414138">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style><div role="note" class="hatnote navigation-not-searchable">Glavni članak: <a href="/wiki/%D0%9C%D0%B5%D0%B4%D0%B8%D1%98%D0%B0%D0%BD%D0%B0" class="mw-disambig" title="Медијана">Medijana</a></div> <p>Aritmetička sredina se može uporediti sa <a href="/wiki/Median" class="mw-redirect" title="Median">medijanom</a>. Medijana je definisana tako da više od polovine vrednosti nije veće od medijane, a ne više od polovine manje od medijane. Ako se elementi u podacima <a href="/wiki/Arithmetic_progression" class="mw-redirect" title="Arithmetic progression">aritmetički povećavaju</a>, kada su postavljeni nekim redom, onda su medijana i aritmetički prosek jednaki. Na primer, razmotrite uzorak podataka <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {1,2,3,4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {1,2,3,4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6821b4deaf83d813729c78a037ed130761869cfa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.752ex; height:2.509ex;" alt="{\displaystyle {1,2,3,4}}" /></span>. Prosek je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2,5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>,</mo> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2,5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c59a51fe622511106e9fff8adc6d8395ac1d003f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.359ex; height:2.509ex;" alt="{\displaystyle 2,5}" /></span>, kao i medijana. Međutim, kada se uzme u obzir uzorak koji se ne može rasporediti tako da se aritmetički povećava, kao što je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {1,2,4,8,16}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>4</mn> <mo>,</mo> <mn>8</mn> <mo>,</mo> <mn>16</mn> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {1,2,4,8,16}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4482f843f8f25442889e6c50a275ecb05939e772" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.11ex; height:2.509ex;" alt="{\displaystyle {1,2,4,8,16}}" /></span>, medijana i aritmetički prosek mogu značajno da se razlikuju. U ovom slučaju, aritmetički prosek je 6,2, dok je medijana 4. Generalno, prosečna vrednost može značajno da varira od većine vrednosti u uzorku, i može biti veća ili manja od većine njih. </p><p>Primene ovog fenomena postoje u mnogim oblastima. Na primer, od 1980-ih, medijana prihoda u Sjedinjenim Državama je rasla sporije od aritmetičkog proseka prihoda.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Generalizacije">Generalizacije</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=5" title="Уредите одељак „Generalizacije”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=5" title="Уреди извор одељка: Generalizacije"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Ponderisana_aritmetička_sredina"><span id="Ponderisana_aritmeti.C4.8Dka_sredina"></span>Ponderisana aritmetička sredina</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=6" title="Уредите одељак „Ponderisana aritmetička sredina”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=6" title="Уреди извор одељка: Ponderisana aritmetička sredina"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r24414138" /><div role="note" class="hatnote navigation-not-searchable">Главни чланак: <a href="/w/index.php?title=Ponderisani_prosek&action=edit&redlink=1" class="new" title="Ponderisani prosek (страница не постоји)">Ponderisani prosek</a></div> <p>Ponderisani prosek, ili ponderisana srednja vrednost, je prosek u kome se neke tačke podataka više računaju od drugih, jer im se pridaje veća težina u proračunu.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Na primer, aritmetička sredina od <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/991e33c6e207b12546f15bdfee8b5726eafbbb2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 3}" /></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29483407999b8763f0ea335cf715a6a5e809f44b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 5}" /></span> je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {(3+5)}{2}}=4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>3</mn> <mo>+</mo> <mn>5</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {(3+5)}{2}}=4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22899e3546369807868735c55abd6f0c83d5f0bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.072ex; height:5.676ex;" alt="{\displaystyle {\frac {(3+5)}{2}}=4}" /></span>, ili ekvivalentno <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {1}{2}}\cdot 3\right)+\left({\frac {1}{2}}\cdot 5\right)=4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>⋅</mo> <mn>3</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>⋅</mo> <mn>5</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {1}{2}}\cdot 3\right)+\left({\frac {1}{2}}\cdot 5\right)=4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b8e2becfec73d109e5596daa4eb1b714139a148" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:23.624ex; height:6.176ex;" alt="{\displaystyle \left({\frac {1}{2}}\cdot 3\right)+\left({\frac {1}{2}}\cdot 5\right)=4}" /></span>. Nasuprot tome, <i>ponderisana</i> srednja vrednost u kojoj prvi broj dobija, na primer, dvostruko veću težinu od drugog (možda zato što se pretpostavlja da se pojavljuje dvostruko češće u opštoj populaciji iz koje su ovi brojevi uzorkovani) bila bi izračunata kao <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {2}{3}}\cdot 3\right)+\left({\frac {1}{3}}\cdot 5\right)={\frac {11}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> <mo>⋅</mo> <mn>3</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <mo>⋅</mo> <mn>5</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>11</mn> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {2}{3}}\cdot 3\right)+\left({\frac {1}{3}}\cdot 5\right)={\frac {11}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/423c22ae22080f40e33af5ffb47abfa810f3f97d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.623ex; height:6.176ex;" alt="{\displaystyle \left({\frac {2}{3}}\cdot 3\right)+\left({\frac {1}{3}}\cdot 5\right)={\frac {11}{3}}}" /></span>. Ovde su težine, koje se nužno zbrajaju sa vrednošću jedan, jesu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (2/3)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (2/3)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6dcb6a222de0a8e1cf8963c699a0967cc4440951" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.297ex; height:2.843ex;" alt="{\displaystyle (2/3)}" /></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (1/3)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1/3)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6141fc2798e0743c6774f94fab9b16e95acaeef5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.297ex; height:2.843ex;" alt="{\displaystyle (1/3)}" /></span>, pri čemu je prva duplo veća od druge. Aritmetička sredina (ponekad se naziva „neponderisani prosek“ ili „jednako ponderisani prosek“) može se tumačiti kao poseban slučaj ponderisanog proseka u kome su sve težine jednake jedna drugoj (jednake <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a11cfb2fdb143693b1daf78fcb5c11a023cb1c55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{2}}}" /></span> u gornjem primeru, i jednake sa <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf0aefecf48d43fdedd71e318ae6129bd67be252" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.231ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{n}}}" /></span> u situaciji sa <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" /></span> usrednjenih brojeva). </p> <div class="mw-heading mw-heading3"><h3 id="Kontinuirane_raspodele_verovatnoće"><span id="Kontinuirane_raspodele_verovatno.C4.87e"></span>Kontinuirane raspodele verovatnoće</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=7" title="Уредите одељак „Kontinuirane raspodele verovatnoće”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=7" title="Уреди извор одељка: Kontinuirane raspodele verovatnoće"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/%D0%94%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Comparison_mean_median_mode.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Comparison_mean_median_mode.svg/300px-Comparison_mean_median_mode.svg.png" decoding="async" width="300" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Comparison_mean_median_mode.svg/450px-Comparison_mean_median_mode.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Comparison_mean_median_mode.svg/600px-Comparison_mean_median_mode.svg.png 2x" data-file-width="512" data-file-height="384" /></a><figcaption>Poređenje dve <a href="/w/index.php?title=Log-normal_distribution&action=edit&redlink=1" class="new" title="Log-normal distribution (страница не постоји)">log-normalne raspodele</a> sa jednakom <a href="/wiki/Median" class="mw-redirect" title="Median">medijanom</a>, ali različitom <a href="/wiki/Skewness" class="mw-redirect" title="Skewness">iskrivljenošc</a>́u, što rezultira različitim <a href="/wiki/Mean" class="mw-redirect" title="Mean">srednjim vrednostima</a> i <a href="/wiki/Mode_(statistics)" class="mw-redirect" title="Mode (statistics)">modovima</a> </figcaption></figure> <p>Ako numeričko svojstvo, i bilo koji uzorak podataka iz njega, može da poprimi bilo koju vrednost iz neprekidnog opsega, umesto, na primer, samo celih brojeva, onda se <a href="/wiki/Probability" class="mw-redirect" title="Probability">verovatnoća</a> da broj padne u neki opseg mogućih vrednosti može opisati integracijom <a href="/wiki/Continuous_probability_distribution" class="mw-redirect" title="Continuous probability distribution">kontinuirane raspodele verovatnoće</a> u ovom opsegu, čak i kada je naivna verovatnoća za broj uzorka koji uzima jednu određenu vrednost od beskonačno mnogo nula. Analog ponderisanog proseka u ovom kontekstu, u kome postoji beskonačan broj mogućnosti za preciznu vrednost promenljive u svakom opsegu, naziva se <i>sredinom distribucije verovatnoće.</i> Raspodela verovatnoće koja se najčešće sreće naziva se <a href="/wiki/Normal_distribution" class="mw-redirect" title="Normal distribution">normalna raspodela</a>; ona ima svojstvo da su sve mere njegove centralne tendencije, uključujući ne samo srednju vrednost, već i gore pomenutu medijanu i <a href="/wiki/Mode_(statistics)" class="mw-redirect" title="Mode (statistics)">mod</a> (tri M-a<sup id="cite_ref-ThreeMs_10-0" class="reference"><a href="#cite_note-ThreeMs-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>), jednake jedna drugoj. Ova jednakost ne važi za druge distribucije verovatnoće, kao što je ilustrovano za <a href="/w/index.php?title=Log-normal_distribution&action=edit&redlink=1" class="new" title="Log-normal distribution (страница не постоји)">log-normalnu raspodelu</a> ovde. </p> <div class="mw-heading mw-heading3"><h3 id="Uglovi">Uglovi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=8" title="Уредите одељак „Uglovi”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=8" title="Уреди извор одељка: Uglovi"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Posebna pažnja se mora obratiti kada koristite ciklični podaci, kao što su faze ili <a href="/wiki/%D0%A3%D0%B3%D0%B0%D0%BE" title="Угао">uglovi</a>. Naivno uzimanje aritmetičke sredine od 1° i 359° daje rezultat od 180°. Ovo nije tačno iz dva razloga: </p> <ul><li>Prvo, merenja ugla su definisana samo do aditivne konstante od <a href="/wiki/Degree_(angle)" class="mw-redirect" title="Degree (angle)">360°</a> (ili 2π, ako se meri u <a href="/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%98%D0%B0%D0%BD" title="Радијан">radijanima</a>). Tako bi se mogli lako nazvati 1° i −1°, ili 361° i 719°, jer svaki od njih daje drugačiji prosek.</li> <li>Drugo, u ovoj situaciji, 0° (ekvivalentno, 360°) je geometrijski bolja prosečna vrednost: oko nje je manja <a href="/w/index.php?title=Statistical_dispersion&action=edit&redlink=1" class="new" title="Statistical dispersion (страница не постоји)">disperzija</a> (tačke su istovremeno 1° od njega, i 179° od 180°, pretpostavljeni prosek).</li></ul> <p>U opštoj primeni, takav previd će dovesti do toga da se prosečna vrednost veštački pomera ka sredini numeričkog opsega. Rešenje ovog problema je korišćenje formulacije optimizacije (odnosno, definisanje srednje vrednosti kao centralne tačke: tačka oko koje ima najmanje disperzije) i redefinisanje razlike kao modularne udaljenosti (tj. rastojanje na kružnici: tako da je modularno rastojanje između 1° i 359° 2°, a ne 358°). </p> <div class="mw-heading mw-heading2"><h2 id="Simboli_i_kodiranje">Simboli i kodiranje</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=9" title="Уредите одељак „Simboli i kodiranje”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=9" title="Уреди извор одељка: Simboli i kodiranje"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Aritmetička sredina se često označava linijom (takođe <a href="/wiki/Vinculum_(symbol)" class="mw-redirect" title="Vinculum (symbol)">vinkulum</a> ili <a href="/w/index.php?title=Macron_(diacritic)&action=edit&redlink=1" class="new" title="Macron (diacritic) (страница не постоји)">makron</a>), na primer kao u <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/466e03e1c9533b4dab1b9949dad393883f385d80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:2.009ex;" alt="{\displaystyle {\bar {x}}}" /></span> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /></span> nadvučeno).<sup id="cite_ref-JM_6-2" class="reference"><a href="#cite_note-JM-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Neki softverski paketi (<a href="/w/index.php?title=Text_processing&action=edit&redlink=1" class="new" title="Text processing (страница не постоји)">tekst procesori</a>, <a href="/wiki/Web_browser" class="mw-redirect" title="Web browser">veb pretraživači</a>) uvek ne prikazuju pravilno simbol x̄. Na primer, simbol x̄ u <a href="/wiki/HTML" title="HTML">HTML</a>-u je zapravo kombinacija dva koda – osnovnog slova x plus koda za liniju iznad (&#772; or ¯).<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>U nekim tekstovima, kao što su <a href="/wiki/PDF" title="PDF">pdf</a>-ovi, simbol x̄ može biti zamenjen simbolom <a href="/w/index.php?title=Euro_coins&action=edit&redlink=1" class="new" title="Euro coins (страница не постоји)">centa</a> (¢) (<a href="/wiki/Unicode" title="Unicode">Unicode</a> &#162), kada se kopira u tekstualni procesor kao što je <a href="/wiki/Microsoft_Word" title="Microsoft Word">Majkrosoft Vord</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Primena">Primena</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=10" title="Уредите одељак „Primena”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=10" title="Уреди извор одељка: Primena"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b> Aritmetička sredina </b> se najviše koristi od svih matematičkih sredina u svakodnevnom životu. Ovu sredinu najčešće koristimo kada hoćemo da izračunamo <i>prosek</i> nečega, tako što sve te brojeve saberemo a onda ih podelimo brojem koliko ih ima. </p> <div class="mw-heading mw-heading2"><h2 id="Primeri">Primeri</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=11" title="Уредите одељак „Primeri”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=11" title="Уреди извор одељка: Primeri"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Primer_1">Primer 1</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=12" title="Уредите одељак „Primer 1”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=12" title="Уреди извор одељка: Primer 1"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>D = (1, 3, 6, 7, 18)</dd></dl> <p>Skup D ima 5 članova čiji zbir je 35, a <i>aritmetička sredina</i> je 7. </p> <div class="mw-heading mw-heading3"><h3 id="Primer_2">Primer 2</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=13" title="Уредите одељак „Primer 2”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=13" title="Уреди извор одељка: Primer 2"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ako u dnevniku u osnovnoj školi iz matematike imamo ocene 5, 5, 3, 2, prosek računamo ovako: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={5+5+3+2 \over 4}={15 \over 4}=3.75.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>5</mn> <mo>+</mo> <mn>5</mn> <mo>+</mo> <mn>3</mn> <mo>+</mo> <mn>2</mn> </mrow> <mn>4</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>15</mn> <mn>4</mn> </mfrac> </mrow> <mo>=</mo> <mn>3.75.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={5+5+3+2 \over 4}={15 \over 4}=3.75.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/675c34045f3209c35159d157faa32acd8f4c7a52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:32.988ex; height:5.176ex;" alt="{\displaystyle A={5+5+3+2 \over 4}={15 \over 4}=3.75.}" /></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Vidi_još"><span id="Vidi_jo.C5.A1"></span>Vidi još</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=14" title="Уредите одељак „Vidi još”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=14" title="Уреди извор одељка: Vidi još"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%D0%A5%D0%B0%D1%80%D0%BC%D0%BE%D0%BD%D0%B8%D1%98%D1%81%D0%BA%D0%B0_%D1%81%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D0%B0" title="Хармонијска средина">Harmonijska sredina</a></li> <li><a href="/wiki/Geometrijska_sredina" title="Geometrijska sredina">Geometrijska sredina</a></li> <li><a href="/wiki/%D0%9D%D0%B5%D1%98%D0%B5%D0%B4%D0%BD%D0%B0%D0%BA%D0%BE%D1%81%D1%82_%D0%B8%D0%B7%D0%BC%D0%B5%D1%92%D1%83_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%BD%D0%B8%D1%85_%D1%81%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D0%B0" class="mw-redirect" title="Неједнакост између бројевних средина">Nejednakost između brojevnih sredina</a></li> <li><a href="/wiki/%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BD%D0%B0_%D1%81%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D0%B0" title="Квадратна средина">Kvadratna sredina</a></li> <li><a href="/wiki/%D0%9A%D1%83%D0%B1%D0%BD%D0%B0_%D1%81%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D0%B0" title="Кубна средина">Kubna sredina</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Reference">Reference</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=15" title="Уредите одељак „Reference”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=15" title="Уреди извор одељка: Reference"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r28440201">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><cite class="citation book">Jacobs, Harold R. (1994). <a rel="nofollow" class="external text" href="https://archive.org/details/mathematicshuman0000jaco"><i>Mathematics: A Human Endeavor</i></a> (Third изд.). <a href="/w/index.php?title=W._H._Freeman&action=edit&redlink=1" class="new" title="W. H. Freeman (страница не постоји)">W. H. Freeman</a>. стр. <a rel="nofollow" class="external text" href="https://archive.org/details/mathematicshuman0000jaco/page/547">547</a>. <a href="/wiki/Me%C4%91unarodni_standardni_broj_knjige" title="Međunarodni standardni broj knjige">ISBN</a> <a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0%D0%BC%D0%BF%D0%B0%D0%BD%D0%B8_%D0%B8%D0%B7%D0%B2%D0%BE%D1%80%D0%B8/0-7167-2426-X" title="Посебно:Штампани извори/0-7167-2426-X">0-7167-2426-X</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.aufirst=Harold+R.&rft.aulast=Jacobs&rft.btitle=Mathematics%3A+A+Human+Endeavor&rft.date=1994&rft.edition=Third&rft.genre=book&rft.isbn=0-7167-2426-X&rft.pages=547&rft.pub=W.+H.+Freeman&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmathematicshuman0000jaco&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Matt Friehauf, Mikaela Hertel, Juan Liu, and Stacey Luong <cite class="citation web"><a rel="nofollow" class="external text" href="https://sites.math.washington.edu/~julia/teaching/445_Spring2013/ConstructionsI.pdf#page=6&zoom=80,-502,802">„On Compass and Straightedge Constructions: Means”</a> <span style="font-size:85%;">(PDF)</span>. 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Приступљено <span class="nowrap">14. 6. 2018</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.btitle=On+Compass+and+Straightedge+Constructions%3A+Means&rft.date=2013&rft.genre=unknown&rft.pub=UNIVERSITY+of+WASHINGTON%2C+DEPARTMENT+OF+MATHEMATICS&rft_id=https%3A%2F%2Fsites.math.washington.edu%2F~julia%2Fteaching%2F445_Spring2013%2FConstructionsI.pdf%23page%3D6%26zoom%3D80%2C-502%2C802&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">CS1 одржавање: Формат датума (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1_%D0%BE%D0%B4%D1%80%D0%B6%D0%B0%D0%B2%D0%B0%D1%9A%D0%B5:_%D0%A4%D0%BE%D1%80%D0%BC%D0%B0%D1%82_%D0%B4%D0%B0%D1%82%D1%83%D0%BC%D0%B0" title="Категорија:CS1 одржавање: Формат датума">веза</a>)</span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://mathcs.clarku.edu/~djoyce/java/elements/bookVI/propVI13.html">„Euclid, Book VI, Proposition 13”</a>. David E. Joyce, Clark University. 2013<span class="reference-accessdate">. Приступљено <span class="nowrap">19. 7. 2019</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.btitle=Euclid%2C+Book+VI%2C+Proposition+13&rft.date=2013&rft.genre=unknown&rft.pub=David+E.+Joyce%2C+Clark+University&rft_id=https%3A%2F%2Fmathcs.clarku.edu%2F~djoyce%2Fjava%2Felements%2FbookVI%2FpropVI13.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">CS1 одржавање: Формат датума (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1_%D0%BE%D0%B4%D1%80%D0%B6%D0%B0%D0%B2%D0%B0%D1%9A%D0%B5:_%D0%A4%D0%BE%D1%80%D0%BC%D0%B0%D1%82_%D0%B4%D0%B0%D1%82%D1%83%D0%BC%D0%B0" title="Категорија:CS1 одржавање: Формат датума">веза</a>)</span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20220711015746/https://www.comap.com/FloydVest/Course/PDF/Cons25PO.pdf">„The Average of Rates and the Average Rate”</a> <span style="font-size:85%;">(PDF)</span>. Архивирано из <a rel="nofollow" class="external text" href="https://www.comap.com/FloydVest/Course/PDF/Cons25PO.pdf">оригинала</a> <span style="font-size:85%;">(PDF)</span> 11. 07. 2022. г<span class="reference-accessdate">. Приступљено <span class="nowrap">11. 07. 2022</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.btitle=The+Average+of+Rates+and+the+Average+Rate&rft.genre=unknown&rft_id=https%3A%2F%2Fwww.comap.com%2FFloydVest%2FCourse%2FPDF%2FCons25PO.pdf&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://learningpundits.com/module-view/48-averages/1-tips-on-averages/">„Average: How to calculate Average, Formula, Weighted average”</a>. <i>learningpundits.com</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171229231610/https://learningpundits.com/module-view/48-averages/1-tips-on-averages/">Архивирано</a> из оригинала 29. 12. 2017. г<span class="reference-accessdate">. Приступљено <span class="nowrap">8. 5. 2018</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.atitle=Average%3A+How+to+calculate+Average%2C+Formula%2C+Weighted+average&rft.genre=unknown&rft.jtitle=learningpundits.com&rft_id=https%3A%2F%2Flearningpundits.com%2Fmodule-view%2F48-averages%2F1-tips-on-averages%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">CS1 одржавање: Формат датума (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1_%D0%BE%D0%B4%D1%80%D0%B6%D0%B0%D0%B2%D0%B0%D1%9A%D0%B5:_%D0%A4%D0%BE%D1%80%D0%BC%D0%B0%D1%82_%D0%B4%D0%B0%D1%82%D1%83%D0%BC%D0%B0" title="Категорија:CS1 одржавање: Формат датума">веза</a>)</span></span> </li> <li id="cite_note-JM-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-JM_6-0"><sup><i><b>а</b></i></sup></a> <a href="#cite_ref-JM_6-1"><sup><i><b>б</b></i></sup></a> <a href="#cite_ref-JM_6-2"><sup><i><b>в</b></i></sup></a></span> <span class="reference-text"><cite class="citation book">Medhi, Jyotiprasad (1992). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=bRUwgf_q5RsC"><i>Statistical Methods: An Introductory Text</i></a>. New Age International. стр. 53—58. <a href="/wiki/Me%C4%91unarodni_standardni_broj_knjige" title="Međunarodni standardni broj knjige">ISBN</a> <a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0%D0%BC%D0%BF%D0%B0%D0%BD%D0%B8_%D0%B8%D0%B7%D0%B2%D0%BE%D1%80%D0%B8/9788122404197" title="Посебно:Штампани извори/9788122404197">9788122404197</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.aufirst=Jyotiprasad&rft.aulast=Medhi&rft.btitle=Statistical+Methods%3A+An+Introductory+Text&rft.date=1992&rft.genre=book&rft.isbn=9788122404197&rft.pages=53-58&rft.pub=New+Age+International&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DbRUwgf_q5RsC&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite class="citation web">Weisstein, Eric W. <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/ArithmeticMean.html">„Arithmetic Mean”</a>. <i>mathworld.wolfram.com</i> (на језику: енглески)<span class="reference-accessdate">. Приступљено <span class="nowrap">2020-08-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.atitle=Arithmetic+Mean&rft.aufirst=Eric+W.&rft.aulast=Weisstein&rft.genre=unknown&rft.jtitle=mathworld.wolfram.com&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FArithmeticMean.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite class="citation magazine">Krugman, Paul (4. 6. 2014) [Fall 1992]. <a rel="nofollow" class="external text" href="http://prospect.org/article/rich-right-and-facts-deconstructing-inequality-debate">„The Rich, the Right, and the Facts: Deconstructing the Income Distribution Debate”</a>. <i>The American Prospect</i>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.aufirst=Paul&rft.aulast=Krugman&rft.btitle=The+Rich%2C+the+Right%2C+and+the+Facts%3A+Deconstructing+the+Income+Distribution+Debate&rft.date=2014-06-04&rft.genre=unknown&rft_id=http%3A%2F%2Fprospect.org%2Farticle%2Frich-right-and-facts-deconstructing-inequality-debate&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">CS1 одржавање: Формат датума (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1_%D0%BE%D0%B4%D1%80%D0%B6%D0%B0%D0%B2%D0%B0%D1%9A%D0%B5:_%D0%A4%D0%BE%D1%80%D0%BC%D0%B0%D1%82_%D0%B4%D0%B0%D1%82%D1%83%D0%BC%D0%B0" title="Категорија:CS1 одржавање: Формат датума">веза</a>)</span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://www.britannica.com/science/mean">„Mean”</a>. <i>Encyclopedia Britannica</i> (на језику: енглески)<span class="reference-accessdate">. Приступљено <span class="nowrap">2020-08-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.atitle=Mean&rft.genre=unknown&rft.jtitle=Encyclopedia+Britannica&rft_id=https%3A%2F%2Fwww.britannica.com%2Fscience%2Fmean&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-ThreeMs-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-ThreeMs_10-0">^</a></b></span> <span class="reference-text"><cite class="citation web">Thinkmap Visual Thesaurus (2010-06-30). <a rel="nofollow" class="external text" href="https://www.visualthesaurus.com/cm/lessons/the-three-ms-of-statistics-mode-median-mean/">„The Three M's of Statistics: Mode, Median, Mean June 30, 2010”</a>. <i>www.visualthesaurus.com</i><span class="reference-accessdate">. Приступљено <span class="nowrap">2018-12-03</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.atitle=The+Three+M%27s+of+Statistics%3A+Mode%2C+Median%2C+Mean+June+30%2C+2010&rft.au=Thinkmap+Visual+Thesaurus&rft.date=2010-06-30&rft.genre=unknown&rft.jtitle=www.visualthesaurus.com&rft_id=https%3A%2F%2Fwww.visualthesaurus.com%2Fcm%2Flessons%2Fthe-three-ms-of-statistics-mode-median-mean%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20220331114343/http://www.personal.psu.edu/ejp10/psu/gotunicode/statsym.html">„Notes on Unicode for Stat Symbols”</a>. <i>www.personal.psu.edu</i>. Архивирано из <a rel="nofollow" class="external text" href="http://www.personal.psu.edu/ejp10/psu/gotunicode/statsym.html">оригинала</a> 31. 03. 2022. г<span class="reference-accessdate">. Приступљено <span class="nowrap">2018-10-14</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.atitle=Notes+on+Unicode+for+Stat+Symbols&rft.genre=unknown&rft.jtitle=www.personal.psu.edu&rft_id=http%3A%2F%2Fwww.personal.psu.edu%2Fejp10%2Fpsu%2Fgotunicode%2Fstatsym.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Literatura">Literatura</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=16" title="Уредите одељак „Literatura”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=16" title="Уреди извор одељка: Literatura"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r28440192">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><cite class="citation book">Huff, Darrell (1993). <span class="plainlinks"><a rel="nofollow" class="external text" href="https://archive.org/details/howtoliewithstat00huff"><i>How to Lie with <span class="nowrap">Statistics<span style="padding-left:0.15em"><span typeof="mw:File"><span title="Неопходна слободна регистрација"><img alt="Неопходна слободна регистрација" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Lock-blue-alt-2.svg/20px-Lock-blue-alt-2.svg.png" decoding="async" width="9" height="14" class="mw-file-element" data-file-width="512" data-file-height="813" /></span></span></span></span></i></a></span>. W. W. Norton. <a href="/wiki/Me%C4%91unarodni_standardni_broj_knjige" title="Međunarodni standardni broj knjige">ISBN</a> <a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0%D0%BC%D0%BF%D0%B0%D0%BD%D0%B8_%D0%B8%D0%B7%D0%B2%D0%BE%D1%80%D0%B8/978-0-393-31072-6" title="Посебно:Штампани извори/978-0-393-31072-6">978-0-393-31072-6</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.aufirst=Darrell&rft.aulast=Huff&rft.btitle=How+to+Lie+with+Statistics&rft.date=1993&rft.genre=book&rft.isbn=978-0-393-31072-6&rft.pub=W.+W.+Norton&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhowtoliewithstat00huff&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book">Bevington, Philip R (1969). <i>Data Reduction and Error Analysis for the Physical Sciences</i>. New York, N.Y.: McGraw-Hill. <a href="/wiki/OCLC" title="OCLC">OCLC</a> <a rel="nofollow" class="external text" href="//www.worldcat.org/oclc/300283069">300283069</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.aufirst=Philip+R&rft.aulast=Bevington&rft.btitle=Data+Reduction+and+Error+Analysis+for+the+Physical+Sciences&rft.date=1969&rft.genre=book&rft.place=New+York%2C+N.Y.&rft.pub=McGraw-Hill&rft_id=info%3Aoclcnum%2F300283069&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book">Strutz, T. (2010). <a rel="nofollow" class="external text" href="https://archive.org/details/datafittinguncer0000tilo"><i>Data Fitting and Uncertainty (A practical introduction to weighted least squares and beyond)</i></a>. Vieweg+Teubner. <a href="/wiki/Me%C4%91unarodni_standardni_broj_knjige" title="Međunarodni standardni broj knjige">ISBN</a> <a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0%D0%BC%D0%BF%D0%B0%D0%BD%D0%B8_%D0%B8%D0%B7%D0%B2%D0%BE%D1%80%D0%B8/978-3-8348-1022-9" title="Посебно:Штампани извори/978-3-8348-1022-9">978-3-8348-1022-9</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.au=Strutz%2C+T.&rft.btitle=Data+Fitting+and+Uncertainty+%28A+practical+introduction+to+weighted+least+squares+and+beyond%29&rft.date=2010&rft.genre=book&rft.isbn=978-3-8348-1022-9&rft.pub=Vieweg%2BTeubner&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fdatafittinguncer0000tilo&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book">Carl-Erik Sarndal; Bengt Swensson, Jan Wretman (1992). <i>Model Assisted Survey Sampling</i>. <a href="/wiki/Me%C4%91unarodni_standardni_broj_knjige" title="Međunarodni standardni broj knjige">ISBN</a> <a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0%D0%BC%D0%BF%D0%B0%D0%BD%D0%B8_%D0%B8%D0%B7%D0%B2%D0%BE%D1%80%D0%B8/9780387975283" title="Посебно:Штампани извори/9780387975283">9780387975283</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.au=Bengt+Swensson%2C+Jan+Wretman&rft.au=Carl-Erik+Sarndal&rft.btitle=Model+Assisted+Survey+Sampling&rft.date=1992&rft.genre=book&rft.isbn=9780387975283&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation journal">Gatz, Donald F.; Smith, Luther (јун 1995). <a rel="nofollow" class="external text" href="https://archive.org/details/sim_atmospheric-environment_1995-06_29_11/page/1185">„The standard error of a weighted mean concentration—I. Bootstrapping vs other methods”</a>. <i>Atmospheric Environment</i>. <b>29</b> (11): 1185—1193. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1995AtmEn..29.1185G">1995AtmEn..29.1185G</a>. <a href="/wiki/Digitalni_identifikator_objekta" title="Digitalni identifikator objekta">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F1352-2310%2894%2900210-C">10.1016/1352-2310(94)00210-C</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.atitle=The+standard+error+of+a+weighted+mean+concentration%E2%80%94I.+Bootstrapping+vs+other+methods&rft.au=Smith%2C+Luther&rft.aufirst=Donald+F.&rft.aulast=Gatz&rft.date=1995&rft.genre=article&rft.issue=11&rft.jtitle=Atmospheric+Environment&rft.pages=1185-1193&rft.volume=29&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsim_atmospheric-environment_1995-06_29_11%2Fpage%2F1185&rft_id=info%3Abibcode%2F1995AtmEn..29.1185G&rft_id=info%3Adoi%2F10.1016%2F1352-2310%2894%2900210-C&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">CS1 одржавање: Формат датума (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1_%D0%BE%D0%B4%D1%80%D0%B6%D0%B0%D0%B2%D0%B0%D1%9A%D0%B5:_%D0%A4%D0%BE%D1%80%D0%BC%D0%B0%D1%82_%D0%B4%D0%B0%D1%82%D1%83%D0%BC%D0%B0" title="Категорија:CS1 одржавање: Формат датума">веза</a>)</span></li> <li><cite class="citation web"><a rel="nofollow" class="external text" href="https://www.gnu.org/software/gsl/manual/html_node/Weighted-Samples.html">„GNU Scientific Library – Reference Manual: Weighted Samples”</a>. <i>Gnu.org</i><span class="reference-accessdate">. Приступљено <span class="nowrap">22. 12. 2017</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.atitle=GNU+Scientific+Library+%E2%80%93+Reference+Manual%3A+Weighted+Samples&rft.genre=unknown&rft.jtitle=Gnu.org&rft_id=https%3A%2F%2Fwww.gnu.org%2Fsoftware%2Fgsl%2Fmanual%2Fhtml_node%2FWeighted-Samples.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">CS1 одржавање: Формат датума (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1_%D0%BE%D0%B4%D1%80%D0%B6%D0%B0%D0%B2%D0%B0%D1%9A%D0%B5:_%D0%A4%D0%BE%D1%80%D0%BC%D0%B0%D1%82_%D0%B4%D0%B0%D1%82%D1%83%D0%BC%D0%B0" title="Категорија:CS1 одржавање: Формат датума">веза</a>)</span></li> <li><cite class="citation journal">Price, George R. (април 1972). <a rel="nofollow" class="external text" href="http://www.dynamics.org/Altenberg/LIBRARY/REPRINTS/Price_extension_AnnHumGenetLond.1972.pdf">„Extension of covariance selection mathematics”</a> <span style="font-size:85%;">(PDF)</span>. <i>Annals of Human Genetics</i>. <b>35</b> (4): 485—490. <a href="/wiki/PMID" title="PMID">PMID</a> <a rel="nofollow" class="external text" href="//www.ncbi.nlm.nih.gov/pubmed/5073694">5073694</a>. <a href="/wiki/Semantic_Scholar" title="Semantic Scholar">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:37828617">37828617</a>. <a href="/wiki/Digitalni_identifikator_objekta" title="Digitalni identifikator objekta">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1469-1809.1957.tb01874.x">10.1111/j.1469-1809.1957.tb01874.x</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.atitle=Extension+of+covariance+selection+mathematics&rft.aufirst=George+R.&rft.aulast=Price&rft.date=1972&rft.genre=article&rft.issue=4&rft.jtitle=Annals+of+Human+Genetics&rft.pages=485-490&rft.volume=35&rft_id=http%3A%2F%2Fwww.dynamics.org%2FAltenberg%2FLIBRARY%2FREPRINTS%2FPrice_extension_AnnHumGenetLond.1972.pdf&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A37828617&rft_id=info%3Adoi%2F10.1111%2Fj.1469-1809.1957.tb01874.x&rft_id=info%3Apmid%2F5073694&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">CS1 одржавање: Формат датума (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1_%D0%BE%D0%B4%D1%80%D0%B6%D0%B0%D0%B2%D0%B0%D1%9A%D0%B5:_%D0%A4%D0%BE%D1%80%D0%BC%D0%B0%D1%82_%D0%B4%D0%B0%D1%82%D1%83%D0%BC%D0%B0" title="Категорија:CS1 одржавање: Формат датума">веза</a>)</span></li> <li>Mark Galassi, Jim Davies, James Theiler, Brian Gough, Gerard Jungman, Michael Booth, and Fabrice Rossi. <a rel="nofollow" class="external text" href="https://www.gnu.org/software/gsl/manual">GNU Scientific Library - Reference manual, Version 1.15</a>, 2011.</li></ul> <p><a rel="nofollow" class="external text" href="https://www.gnu.org/software/gsl/manual/html_node/Weighted-Samples.html">Sec. 21.7 Weighted Samples</a> </p> <ul><li><cite class="citation book">James, Frederick (2006). <i>Statistical Methods in Experimental Physics</i> (2nd изд.). Singapore: World Scientific. <a href="/wiki/Me%C4%91unarodni_standardni_broj_knjige" title="Međunarodni standardni broj knjige">ISBN</a> <a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0%D0%BC%D0%BF%D0%B0%D0%BD%D0%B8_%D0%B8%D0%B7%D0%B2%D0%BE%D1%80%D0%B8/981-270-527-9" title="Посебно:Штампани извори/981-270-527-9">981-270-527-9</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3AAritmeti%C4%8Dka+sredina&rft.aufirst=Frederick&rft.aulast=James&rft.btitle=Statistical+Methods+in+Experimental+Physics&rft.date=2006&rft.edition=2nd&rft.genre=book&rft.isbn=981-270-527-9&rft.place=Singapore&rft.pub=World+Scientific&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li></ul> <p><br /> </p> </div> <div class="mw-heading mw-heading2"><h2 id="Spoljašnje_veze"><span id="Spolja.C5.A1nje_veze"></span>Spoljašnje veze</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&veaction=edit&section=17" title="Уредите одељак „Spoljašnje veze”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aritmeti%C4%8Dka_sredina&action=edit&section=17" title="Уреди извор одељка: Spoljašnje veze"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r25554621">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9;display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r25554968">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/60px-Commons-logo.svg.png 1.5x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist"><span style="font-weight:bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Arithmetic_mean" class="extiw" title="commons:Category:Arithmetic mean">Aritmetička sredina</a></span> на <a href="https://commons.wikimedia.org/wiki/%D0%93%D0%BB%D0%B0%D0%B2%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B0" class="extiw" title="commons:Главна страна">Викимедијиној остави</a>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.sengpielaudio.com/calculator-geommean.htm">Calculations and comparisons between arithmetic mean and geometric mean of two numbers</a></li> <li><a rel="nofollow" class="external text" href="http://www.fxsolver.com/browse/formulas/Arithmetic+Mean">Calculate the arithmetic mean of a series of numbers on fxSolver</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150924020300/http://www.fxsolver.com/browse/formulas/Arithmetic+Mean">Архивирано</a> на веб-сајту <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> (24. септембар 2015)</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r25469611">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist 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