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<span>Alternar subsección Definición</span> </button> <ul id="toc-Definición-sublist" class="vector-toc-list"> <li id="toc-Propiedad" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Propiedad"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Propiedad</span> </div> </a> <ul id="toc-Propiedad-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Aplicaciones" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aplicaciones"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Aplicaciones</span> </div> </a> <button aria-controls="toc-Aplicaciones-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>Alternar subsección Aplicaciones</span> </button> <ul id="toc-Aplicaciones-sublist" class="vector-toc-list"> <li id="toc-Valor_eficaz_de_una_corriente_alterna" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Valor_eficaz_de_una_corriente_alterna"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Valor eficaz de una corriente alterna</span> </div> </a> <ul id="toc-Valor_eficaz_de_una_corriente_alterna-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Media_cuadrática_de_la_velocidad_de_un_gas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Media_cuadrática_de_la_velocidad_de_un_gas"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Media cuadrática de la velocidad de un gas</span> </div> </a> <ul id="toc-Media_cuadrática_de_la_velocidad_de_un_gas-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Véase_también" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Véase_también"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Véase también</span> </div> </a> <ul id="toc-Véase_también-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referencias" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referencias"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Referencias</span> </div> </a> <ul id="toc-Referencias-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="Contenidos" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <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="Cambiar a la tabla de contenidos" > <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">Cambiar a la tabla de contenidos</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">Media cuadrática</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="Ir a un artículo en otro idioma. Disponible en 39 idiomas" > <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-39" 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">39 idiomas</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/%D8%AC%D8%B0%D8%B1_%D9%85%D8%AA%D9%88%D8%B3%D8%B7_%D9%85%D8%B1%D8%A8%D8%B9" title="جذر متوسط مربع (árabe)" lang="ar" hreflang="ar" data-title="جذر متوسط مربع" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A1%D1%8F%D1%80%D1%8D%D0%B4%D0%BD%D1%8F%D0%B5_%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D0%B5" title="Сярэдняе квадратычнае (Belarusian (Taraškievica orthography))" lang="be-tarask" hreflang="be-tarask" data-title="Сярэдняе квадратычнае" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</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%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%BE" title="Средно квадратично (búlgaro)" lang="bg" hreflang="bg" data-title="Средно квадратично" data-language-autonym="Български" data-language-local-name="búlgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%B0%E0%A7%8D%E0%A6%97%E0%A6%AE%E0%A7%82%E0%A6%B2_%E0%A6%97%E0%A6%A1%E0%A6%BC_%E0%A6%AC%E0%A6%B0%E0%A7%8D%E0%A6%97" title="বর্গমূল গড় বর্গ (bengalí)" lang="bn" hreflang="bn" data-title="বর্গমূল গড় বর্গ" data-language-autonym="বাংলা" data-language-local-name="bengalí" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Mitjana_quadr%C3%A0tica" title="Mitjana quadràtica (catalán)" lang="ca" hreflang="ca" data-title="Mitjana quadràtica" data-language-autonym="Català" data-language-local-name="catalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Kvadratick%C3%BD_pr%C5%AFm%C4%9Br" title="Kvadratický průměr (checo)" lang="cs" hreflang="cs" data-title="Kvadratický průměr" data-language-autonym="Čeština" data-language-local-name="checo" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Effektiv_v%C3%A6rdi" title="Effektiv værdi (danés)" lang="da" hreflang="da" data-title="Effektiv værdi" data-language-autonym="Dansk" data-language-local-name="danés" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Quadratisches_Mittel" title="Quadratisches Mittel (alemán)" lang="de" hreflang="de" data-title="Quadratisches Mittel" data-language-autonym="Deutsch" data-language-local-name="alemán" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Root_mean_square" title="Root mean square (inglés)" lang="en" hreflang="en" data-title="Root mean square" data-language-autonym="English" data-language-local-name="inglés" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kvadrata_avera%C4%9Do" title="Kvadrata averaĝo (esperanto)" lang="eo" hreflang="eo" data-title="Kvadrata averaĝo" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Ruutkeskmine" title="Ruutkeskmine (estonio)" lang="et" hreflang="et" data-title="Ruutkeskmine" data-language-autonym="Eesti" data-language-local-name="estonio" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Batezbesteko_koadratiko" title="Batezbesteko koadratiko (euskera)" lang="eu" hreflang="eu" data-title="Batezbesteko koadratiko" data-language-autonym="Euskara" data-language-local-name="euskera" 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/%D8%AC%D8%B0%D8%B1_%D9%85%DB%8C%D8%A7%D9%86%DA%AF%DB%8C%D9%86_%D9%85%D8%B1%D8%A8%D8%B9%D8%A7%D8%AA" title="جذر میانگین مربعات (persa)" lang="fa" hreflang="fa" data-title="جذر میانگین مربعات" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Neli%C3%B6llinen_keskiarvo" title="Neliöllinen keskiarvo (finés)" lang="fi" hreflang="fi" data-title="Neliöllinen keskiarvo" data-language-autonym="Suomi" data-language-local-name="finés" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Moyenne_quadratique" title="Moyenne quadratique (francés)" lang="fr" hreflang="fr" data-title="Moyenne quadratique" data-language-autonym="Français" data-language-local-name="francés" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A9%D7%95%D7%A8%D7%A9_%D7%9E%D7%9E%D7%95%D7%A6%D7%A2_%D7%94%D7%A8%D7%99%D7%91%D7%95%D7%A2%D7%99%D7%9D" title="שורש ממוצע הריבועים (hebreo)" lang="he" hreflang="he" data-title="שורש ממוצע הריבועים" data-language-autonym="עברית" data-language-local-name="hebreo" 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%B5%E0%A4%B0%E0%A5%8D%E0%A4%97_%E0%A4%AE%E0%A4%BE%E0%A4%A7%E0%A5%8D%E0%A4%AF_%E0%A4%AE%E0%A5%82%E0%A4%B2" title="वर्ग माध्य मूल (hindi)" lang="hi" hreflang="hi" data-title="वर्ग माध्य मूल" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/N%C3%A9gyzetes_k%C3%B6z%C3%A9p" title="Négyzetes közép (húngaro)" lang="hu" hreflang="hu" data-title="Négyzetes közép" data-language-autonym="Magyar" data-language-local-name="húngaro" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Rata-rata_kuadrat" title="Rata-rata kuadrat (indonesio)" lang="id" hreflang="id" data-title="Rata-rata kuadrat" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesio" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BA%8C%E4%B9%97%E5%B9%B3%E5%9D%87%E5%B9%B3%E6%96%B9%E6%A0%B9" title="二乗平均平方根 (japonés)" lang="ja" hreflang="ja" data-title="二乗平均平方根" data-language-autonym="日本語" data-language-local-name="japonés" 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%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D1%82%D1%8B%D2%9B_%D0%BE%D1%80%D1%82%D0%B0%D1%88%D0%B0%D0%BB%D0%B0%D1%80" title="Квадраттық орташалар (kazajo)" lang="kk" hreflang="kk" data-title="Квадраттық орташалар" data-language-autonym="Қазақша" data-language-local-name="kazajo" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%9C%EA%B3%B1%ED%8F%89%EA%B7%A0%EC%A0%9C%EA%B3%B1%EA%B7%BC" title="제곱평균제곱근 (coreano)" lang="ko" hreflang="ko" data-title="제곱평균제곱근" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kwadratisch_gemiddelde" title="Kwadratisch gemiddelde (neerlandés)" lang="nl" hreflang="nl" data-title="Kwadratisch gemiddelde" data-language-autonym="Nederlands" data-language-local-name="neerlandés" 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/Kvadratisk_gjennomsnitt" title="Kvadratisk gjennomsnitt (noruego bokmal)" lang="nb" hreflang="nb" data-title="Kvadratisk gjennomsnitt" data-language-autonym="Norsk bokmål" data-language-local-name="noruego bokmal" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/%C5%9Arednia_kwadratowa" title="Średnia kwadratowa (polaco)" lang="pl" hreflang="pl" data-title="Średnia kwadratowa" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Media_quadr%C3%A0tica" title="Media quadràtica (Piedmontese)" lang="pms" hreflang="pms" data-title="Media quadràtica" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Valor_eficaz" title="Valor eficaz (portugués)" lang="pt" hreflang="pt" data-title="Valor eficaz" data-language-autonym="Português" data-language-local-name="portugués" 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_p%C4%83tratic%C4%83" title="Medie pătratică (rumano)" lang="ro" hreflang="ro" data-title="Medie pătratică" data-language-autonym="Română" data-language-local-name="rumano" 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%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5" title="Среднее квадратическое (ruso)" lang="ru" hreflang="ru" data-title="Среднее квадратическое" data-language-autonym="Русский" data-language-local-name="ruso" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Root_mean_square" title="Root mean square (Simple English)" lang="en-simple" hreflang="en-simple" data-title="Root mean square" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kvadratick%C3%BD_priemer" title="Kvadratický priemer (eslovaco)" lang="sk" hreflang="sk" data-title="Kvadratický priemer" data-language-autonym="Slovenčina" data-language-local-name="eslovaco" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/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 (serbio)" lang="sr" hreflang="sr" data-title="Квадратна средина" data-language-autonym="Српски / srpski" data-language-local-name="serbio" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kvadratiskt_medelv%C3%A4rde" title="Kvadratiskt medelvärde (sueco)" lang="sv" hreflang="sv" data-title="Kvadratiskt medelvärde" data-language-autonym="Svenska" data-language-local-name="sueco" 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%84%E0%B9%88%E0%B8%B2%E0%B9%80%E0%B8%89%E0%B8%A5%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%81%E0%B8%B3%E0%B8%A5%E0%B8%B1%E0%B8%87%E0%B8%AA%E0%B8%AD%E0%B8%87" title="ค่าเฉลี่ยกำลังสอง (tailandés)" lang="th" hreflang="th" data-title="ค่าเฉลี่ยกำลังสอง" data-language-autonym="ไทย" data-language-local-name="tailandés" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Karek%C3%B6k_ortalama" title="Karekök ortalama (turco)" lang="tr" hreflang="tr" data-title="Karekök ortalama" data-language-autonym="Türkçe" data-language-local-name="turco" 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%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%B5" title="Середнє квадратичне (ucraniano)" lang="uk" hreflang="uk" data-title="Середнє квадратичне" data-language-autonym="Українська" data-language-local-name="ucraniano" 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/%DA%86%DA%A9%D9%88%D8%B1%DB%8C_%D8%A7%D9%88%D8%B3%D8%B7" title="چکوری اوسط (urdu)" lang="ur" hreflang="ur" data-title="چکوری اوسط" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Gi%C3%A1_tr%E1%BB%8B_hi%E1%BB%87u_d%E1%BB%A5ng" title="Giá trị hiệu dụng (vietnamita)" lang="vi" hreflang="vi" data-title="Giá trị hiệu dụng" data-language-autonym="Tiếng 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src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/MathematicalMeans.svg/250px-MathematicalMeans.svg.png" decoding="async" width="250" height="140" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/MathematicalMeans.svg/375px-MathematicalMeans.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f7/MathematicalMeans.svg/500px-MathematicalMeans.svg.png 2x" data-file-width="1020" data-file-height="570" /></a><figcaption>Construcción geométrica para hallar las medias <a href="/wiki/Media_aritm%C3%A9tica" title="Media aritmética">aritmética</a> (A), cuadrática (Q), <a href="/wiki/Media_geom%C3%A9trica" title="Media geométrica">geométrica</a> (G) y <a href="/wiki/Media_arm%C3%B3nica" title="Media armónica">armónica</a> (H) de dos números <i>a</i> y <i>b</i>.</figcaption></figure> <p>En <a href="/wiki/Matem%C3%A1ticas" title="Matemáticas">matemáticas</a>, la <b>media cuadrática</b>, <b>valor cuadrático medio</b>, <b>raíz de la media cuadrática</b> o <i><b>RMS</b></i> (del inglés <i>root mean square</i>) es una medida estadística de la magnitud de una cantidad variable. Puede calcularse para una serie de valores discretos o para una <a href="/wiki/Funci%C3%B3n_matem%C3%A1tica" class="mw-redirect" title="Función matemática">función matemática</a> de variable continua por ejemplo movimiento helicoidal. El nombre deriva del hecho de que es la <a href="/wiki/Ra%C3%ADz_cuadrada" title="Raíz cuadrada">raíz cuadrada</a> de la <a href="/wiki/Media_aritm%C3%A9tica" title="Media aritmética">media aritmética</a> de los <a href="/wiki/Cuadrado_(%C3%A1lgebra)" class="mw-redirect" title="Cuadrado (álgebra)">cuadrados</a> de los valores. </p><p>A veces la variable toma valores positivos y negativos, como ocurre, por ejemplo, en los <a href="/wiki/Errores_de_medida" class="mw-redirect" title="Errores de medida">errores de medida</a>. En tal caso se puede estar interesado en obtener un promedio que no recoja los efectos del signo. Este problema se resuelve, mediante la denominada media cuadrática. Consiste en elevar al cuadrado todas las observaciones (así los signos negativos desaparecen), en obtener después su media aritmética y en extraer, finalmente, la raíz cuadrada de dicha media para volver a la <a href="/wiki/Unidad_de_medida" title="Unidad de medida">unidad de medida</a> original. La <a href="/wiki/Desviaci%C3%B3n_est%C3%A1ndar" class="mw-redirect" title="Desviación estándar">desviación estándar</a> es una media cuadrática. </p><p>Otras medias <a href="/wiki/Estad%C3%ADstica" title="Estadística">estadísticas</a> son la <a href="/wiki/Media_ponderada" title="Media ponderada">media ponderada</a>, la <a href="/wiki/Media_generalizada" title="Media generalizada">media generalizada</a>, <a href="/wiki/Media_arm%C3%B3nica" title="Media armónica">media armónica</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definición"><span id="Definici.C3.B3n"></span>Definición</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Media_cuadr%C3%A1tica&action=edit&section=1" title="Editar sección: Definición"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La media cuadrática para una colección de N valores {<i>x</i><sub>1</sub>, <i>x</i><sub>2</sub>, ... , <i>x</i><sub>n</sub>} de una <a href="/wiki/Variable_discreta_y_variable_continua" title="Variable discreta y variable continua">variable discreta</a> x,<sup id="cite_ref-1" class="reference separada"><a href="#cite_note-1"><span class="corchete-llamada">[</span>1<span class="corchete-llamada">]</span></a></sup> viene dada por la fórmula <b>(1)</b>: </p> <center><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_{\mathrm {RMS} }={\sqrt {{1 \over N}\sum _{i=1}^{N}x_{i}^{2}}}={\sqrt {{x_{1}^{2}+x_{2}^{2}+\cdots +x_{N}^{2}} \over N}}\qquad \qquad (1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">S</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <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> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mi>N</mi> </mfrac> </msqrt> </mrow> <mspace width="2em" /> <mspace width="2em" /> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{\mathrm {RMS} }={\sqrt {{1 \over N}\sum _{i=1}^{N}x_{i}^{2}}}={\sqrt {{x_{1}^{2}+x_{2}^{2}+\cdots +x_{N}^{2}} \over N}}\qquad \qquad (1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae6eb0857eee5544af02d275f716b35c13e2dfb3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:57.711ex; height:8.009ex;" alt="{\displaystyle x_{\mathrm {RMS} }={\sqrt {{1 \over N}\sum _{i=1}^{N}x_{i}^{2}}}={\sqrt {{x_{1}^{2}+x_{2}^{2}+\cdots +x_{N}^{2}} \over N}}\qquad \qquad (1)}"></span></center> <p>Para una función de variable continua <b>f(t)</b> definida sobre el intervalo T<sub>1</sub> ≤ <b>t</b> ≤ T<sub>2</sub> viene dada por la expresión: </p> <center><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_{\mathrm {rms} }={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{[f(t)]}^{2}\,dt}}}.\qquad \qquad (2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msubsup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> </mrow> </msqrt> </mrow> <mo>.</mo> <mspace width="2em" /> <mspace width="2em" /> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{\mathrm {rms} }={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{[f(t)]}^{2}\,dt}}}.\qquad \qquad (2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b37a77ca01efabb749260a3b6cc838d7a1e02c40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:45.035ex; height:7.676ex;" alt="{\displaystyle x_{\mathrm {rms} }={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{[f(t)]}^{2}\,dt}}}.\qquad \qquad (2)}"></span></center> <div class="mw-heading mw-heading3"><h3 id="Propiedad">Propiedad</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Media_cuadr%C3%A1tica&action=edit&section=2" title="Editar sección: Propiedad"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hay una relación de orden de las medias obtenidas de una misma colección de valores </p> <dl><dd><dl><dd><dl><dd>H≤ G ≤ A ≤ Q , donde H es la <a href="/wiki/Media_arm%C3%B3nica" title="Media armónica">media armónica</a>; G, la <a href="/wiki/Media_geom%C3%A9trica" title="Media geométrica">media geométrica</a>; A, la <a href="/wiki/Media_aritm%C3%A9tica" title="Media aritmética">media aritmética</a> ; Q, la media cuadrática<sup id="cite_ref-2" class="reference separada"><a href="#cite_note-2"><span class="corchete-llamada">[</span>2<span class="corchete-llamada">]</span></a></sup></dd></dl></dd></dl></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Aplicaciones">Aplicaciones</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Media_cuadr%C3%A1tica&action=edit&section=3" title="Editar sección: Aplicaciones"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Valor_eficaz_de_una_corriente_alterna">Valor eficaz de una corriente alterna</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Media_cuadr%C3%A1tica&action=edit&section=4" title="Editar sección: Valor eficaz de una corriente alterna"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="noprint AP rellink"><span style="font-size:88%">Artículo principal:</span> <i><a href="/wiki/Valor_eficaz" title="Valor eficaz"> Valor eficaz</a></i></div> <p>Generalmente, el valor eficaz es usado en <a href="/wiki/F%C3%ADsica" title="Física">física</a> e <a href="/wiki/Ingenier%C3%ADa" title="Ingeniería">ingeniería</a>, aunque tiene otros usos. </p> <div class="mw-heading mw-heading3"><h3 id="Media_cuadrática_de_la_velocidad_de_un_gas"><span id="Media_cuadr.C3.A1tica_de_la_velocidad_de_un_gas"></span>Media cuadrática de la velocidad de un gas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Media_cuadr%C3%A1tica&action=edit&section=5" title="Editar sección: Media cuadrática de la velocidad de un gas"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="noprint AP rellink"><span style="font-size:88%">Artículo principal:</span> <i><a href="/wiki/Ra%C3%ADz_de_la_velocidad_cuadr%C3%A1tica_media" class="mw-redirect" title="Raíz de la velocidad cuadrática media"> Raíz de la velocidad cuadrática media</a></i></div> <p>En <a href="/wiki/F%C3%ADsica" title="Física">física</a>, la <b>media cuadrática de la velocidad de un gas</b> se define como la raíz cuadrada de la media de los cuadrados de las velocidades de las moléculas de un <a href="/wiki/Gas" title="Gas">gas</a>. La velocidad RMS de un <a href="/wiki/Gas_ideal" title="Gas ideal">gas ideal</a> es <a href="/wiki/Distribuci%C3%B3n_de_Boltzmann" title="Distribución de Boltzmann">calculada</a> usando la siguiente ecuación: </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 {v_{\mathrm {RMS} }}={\sqrt {3kT \over {M}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">S</mi> </mrow> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>3</mn> <mi>k</mi> <mi>T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {v_{\mathrm {RMS} }}={\sqrt {3kT \over {M}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/261b8791af593888dda82c03fa3fa1f93af76f6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.259ex; height:6.176ex;" alt="{\displaystyle {v_{\mathrm {RMS} }}={\sqrt {3kT \over {M}}}}"></span></dd></dl> <p>donde <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 k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> representa la <a href="/wiki/Constante_de_Boltzmann" title="Constante de Boltzmann">constante de Boltzmann</a> (en este caso, 1.3806503*10<sup>-23</sup>J/K), <i>T</i> es la <a href="/wiki/Temperatura" title="Temperatura">temperatura</a> del gas en <a href="/wiki/Kelvin" title="Kelvin">kelvins</a>, y <i>M</i> es la <a href="/wiki/Masa" title="Masa">masa</a> del gas, medida en <a href="/wiki/Kilogramo" title="Kilogramo">kilogramos</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Véase_también"><span id="V.C3.A9ase_tambi.C3.A9n"></span>Véase también</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Media_cuadr%C3%A1tica&action=edit&section=6" title="Editar sección: Véase también"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Desviaci%C3%B3n_t%C3%ADpica" title="Desviación típica">Desviación típica</a></li> <li><a href="/wiki/Media_geom%C3%A9trica" title="Media geométrica">Media geométrica</a></li> <li><a href="/wiki/Valor_eficaz" title="Valor eficaz">Valor eficaz</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referencias">Referencias</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Media_cuadr%C3%A1tica&action=edit&section=7" title="Editar sección: Referencias"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="listaref" style="list-style-type: decimal;"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Mitacc M, <i>Tópicos de estadística descriptiva y probabilidad</i> [1989]; Perú; pg 86.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Op. 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