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Indicateur de tendance centrale — Wikipédia
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Disponible en 30 langues." > <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-30" 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">30 langues</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%86%D8%B2%D8%B9%D8%A9_%D9%85%D8%B1%D9%83%D8%B2%D9%8A%D8%A9" title="نزعة مركزية – arabe" lang="ar" hreflang="ar" data-title="نزعة مركزية" data-language-autonym="العربية" data-language-local-name="arabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Tend%C3%A8ncia_central" title="Tendència central – catalan" lang="ca" hreflang="ca" data-title="Tendència central" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%BE%DB%8E%D9%88%DB%95%D8%B1%DB%95%DA%A9%D8%A7%D9%86%DB%8C_%DA%95%D9%88%D9%88%DA%A9%D8%B1%D8%AF%D9%86%DB%95_%DA%86%DB%95%D9%82" title="پێوەرەکانی ڕووکردنە چەق – sorani" lang="ckb" hreflang="ckb" data-title="پێوەرەکانی ڕووکردنە چەق" data-language-autonym="کوردی" data-language-local-name="sorani" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Canolduedd" title="Canolduedd – gallois" lang="cy" hreflang="cy" data-title="Canolduedd" data-language-autonym="Cymraeg" data-language-local-name="gallois" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Lagema%C3%9F_(Stochastik)" title="Lagemaß (Stochastik) – allemand" lang="de" hreflang="de" data-title="Lagemaß (Stochastik)" data-language-autonym="Deutsch" data-language-local-name="allemand" 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/Central_tendency" title="Central tendency – anglais" lang="en" hreflang="en" data-title="Central tendency" data-language-autonym="English" data-language-local-name="anglais" 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/Medidas_de_tendencia_central" title="Medidas de tendencia central – espagnol" lang="es" hreflang="es" data-title="Medidas de tendencia central" data-language-autonym="Español" data-language-local-name="espagnol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zentro-joera_(estatistika)" title="Zentro-joera (estatistika) – basque" lang="eu" hreflang="eu" data-title="Zentro-joera (estatistika)" data-language-autonym="Euskara" data-language-local-name="basque" 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%B4%D8%A7%D8%AE%D8%B5%E2%80%8C%D9%87%D8%A7%DB%8C_%D9%85%D8%B1%DA%A9%D8%B2%DB%8C" title="شاخصهای مرکزی – persan" lang="fa" hreflang="fa" data-title="شاخصهای مرکزی" data-language-autonym="فارسی" data-language-local-name="persan" 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/Keskiluku" title="Keskiluku – finnois" lang="fi" hreflang="fi" data-title="Keskiluku" data-language-autonym="Suomi" data-language-local-name="finnois" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Tendencia_central" title="Tendencia central – galicien" lang="gl" hreflang="gl" data-title="Tendencia central" data-language-autonym="Galego" data-language-local-name="galicien" 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%93%D7%93_%D7%9E%D7%99%D7%A7%D7%95%D7%9D_%D7%9E%D7%A8%D7%9B%D7%96%D7%99" title="מדד מיקום מרכזי – hébreu" lang="he" hreflang="he" data-title="מדד מיקום מרכזי" data-language-autonym="עברית" data-language-local-name="hébreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Ukuran_pemusatan_data" title="Ukuran pemusatan data – indonésien" lang="id" hreflang="id" data-title="Ukuran pemusatan data" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésien" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Indice_di_posizione" title="Indice di posizione – italien" lang="it" hreflang="it" data-title="Indice di posizione" data-language-autonym="Italiano" data-language-local-name="italien" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A4%91%EC%8B%AC%EA%B2%BD%ED%96%A5%EC%B9%98" title="중심경향치 – coréen" lang="ko" hreflang="ko" data-title="중심경향치" data-language-autonym="한국어" data-language-local-name="coréen" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Tercondong_pusat" title="Tercondong pusat – malais" lang="ms" hreflang="ms" data-title="Tercondong pusat" data-language-autonym="Bahasa Melayu" data-language-local-name="malais" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Centrummaat" title="Centrummaat – néerlandais" lang="nl" hreflang="nl" data-title="Centrummaat" data-language-autonym="Nederlands" data-language-local-name="néerlandais" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Tendencja_centralna" title="Tendencja centralna – polonais" lang="pl" hreflang="pl" data-title="Tendencja centralna" data-language-autonym="Polski" data-language-local-name="polonais" 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/Tend%C3%AAncia_central" title="Tendência central – portugais" lang="pt" hreflang="pt" data-title="Tendência central" data-language-autonym="Português" data-language-local-name="portugais" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B5%D1%80%D1%8B_%D1%86%D0%B5%D0%BD%D1%82%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B9_%D1%82%D0%B5%D0%BD%D0%B4%D0%B5%D0%BD%D1%86%D0%B8%D0%B8" title="Меры центральной тенденции – russe" lang="ru" hreflang="ru" data-title="Меры центральной тенденции" data-language-autonym="Русский" data-language-local-name="russe" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9A%E0%B7%9A%E0%B6%B1%E0%B7%8A%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%92%E0%B6%9A_%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%80%E0%B6%AB%E0%B6%AD%E0%B7%8F%E0%B7%80" title="කේන්ද්රික ප්රවණතාව – cingalais" lang="si" hreflang="si" data-title="කේන්ද්රික ප්රවණතාව" data-language-autonym="සිංහල" data-language-local-name="cingalais" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Central_tendency" title="Central tendency – Simple English" lang="en-simple" hreflang="en-simple" data-title="Central tendency" 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-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A6%D0%B5%D0%BD%D1%82%D1%80%D0%B0%D0%BB%D0%BD%D0%B0_%D1%82%D0%B5%D0%BD%D0%B4%D0%B5%D0%BD%D1%86%D0%B8%D1%98%D0%B0" title="Централна тенденција – serbe" lang="sr" hreflang="sr" data-title="Централна тенденција" data-language-autonym="Српски / srpski" data-language-local-name="serbe" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Central_tendency" title="Central tendency – soundanais" lang="su" hreflang="su" data-title="Central tendency" data-language-autonym="Sunda" data-language-local-name="soundanais" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Kipimo_cha_mwelekeo_wa_kati" title="Kipimo cha mwelekeo wa kati – swahili" lang="sw" hreflang="sw" data-title="Kipimo cha mwelekeo wa kati" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%95%E0%B1%87%E0%B0%82%E0%B0%A6%E0%B1%8D%E0%B0%B0%E0%B1%80%E0%B0%AF_%E0%B0%AA%E0%B1%8D%E0%B0%B0%E0%B0%B5%E0%B1%83%E0%B0%A4%E0%B1%8D%E0%B0%A4%E0%B0%BF_%E0%B0%AE%E0%B0%BE%E0%B0%AA%E0%B0%A8%E0%B0%BE%E0%B0%B2%E0%B1%81" title="కేంద్రీయ ప్రవృత్తి మాపనాలు – télougou" lang="te" hreflang="te" data-title="కేంద్రీయ ప్రవృత్తి మాపనాలు" data-language-autonym="తెలుగు" data-language-local-name="télougou" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%99%E0%B8%A7%E0%B9%82%E0%B8%99%E0%B9%89%E0%B8%A1%E0%B8%AA%E0%B8%B9%E0%B9%88%E0%B8%AA%E0%B9%88%E0%B8%A7%E0%B8%99%E0%B8%81%E0%B8%A5%E0%B8%B2%E0%B8%87" title="แนวโน้มสู่ส่วนกลาง – thaï" lang="th" hreflang="th" data-title="แนวโน้มสู่ส่วนกลาง" data-language-autonym="ไทย" data-language-local-name="thaï" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A6%D0%B5%D0%BD%D1%82%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0_%D1%82%D0%B5%D0%BD%D0%B4%D0%B5%D0%BD%D1%86%D1%96%D1%8F" title="Центральна тенденція – ukrainien" lang="uk" hreflang="uk" data-title="Центральна тенденція" data-language-autonym="Українська" data-language-local-name="ukrainien" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%9B%86%E4%B8%AD%E8%B6%8B%E5%8A%BF" title="集中趋势 – chinois" lang="zh" hreflang="zh" data-title="集中趋势" data-language-autonym="中文" data-language-local-name="chinois" 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/%E9%9B%86%E4%B8%AD%E8%B6%A8%E5%8B%A2" title="集中趨勢 – cantonais" lang="yue" hreflang="yue" data-title="集中趨勢" data-language-autonym="粵語" data-language-local-name="cantonais" 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/Q734219#sitelinks-wikipedia" title="Modifier les liens interlangues" class="wbc-editpage">Modifier les liens</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="Espaces de noms"> <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 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class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Bernoulli12.png/220px-Bernoulli12.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/1/15/Bernoulli12.png 1.5x" data-file-width="256" data-file-height="192" /></a><figcaption>Diagramme d'une <a href="/wiki/Loi_binomiale" title="Loi binomiale">loi binomiale</a> avec des indicateurs de tendance centrale (comme la <a href="/wiki/Moyenne" title="Moyenne">moyenne</a> au centre).</figcaption></figure> <p>En <a href="/wiki/Statistique" title="Statistique">statistique</a>, un <b>indicateur de tendance centrale</b> est une valeur résumant une <a href="/wiki/S%C3%A9rie_statistique" title="Série statistique">série statistique</a> pour une <a href="/wiki/Variable_quantitative" title="Variable quantitative">variable quantitative</a> ou <a href="/wiki/Variable_ordinale" title="Variable ordinale">ordinale</a>. Les deux principaux sont la <a href="/wiki/Moyenne" title="Moyenne">moyenne</a> et la <a href="/wiki/M%C3%A9diane_(statistiques)" title="Médiane (statistiques)">médiane</a>, mais on trouve parfois aussi la valeur centrale (moyenne des valeurs minimale et maximale) ou le <a href="/wiki/Mode_(statistique)" class="mw-redirect" title="Mode (statistique)">mode</a>. Ce dernier n’étant pas nécessairement <a href="/wiki/Unicit%C3%A9_(math%C3%A9matiques)" title="Unicité (mathématiques)">unique</a> pour une série statistique, sa définition ne s’obtient pas directement comme une <a href="/wiki/Fonction_(math%C3%A9matiques)" title="Fonction (mathématiques)">fonction</a> des termes de la série. </p><p>Un indicateur de tendance centrale est toujours compris entre les valeurs maximale et minimale. Pour une variable numérique, il s’agit en général d’une fonction <a href="/wiki/Lin%C3%A9arit%C3%A9" title="Linéarité">linéaire</a> des valeurs. </p> <div class="mw-heading mw-heading2"><h2 id="Exemples_d'indicateurs"><span id="Exemples_d.27indicateurs"></span>Exemples d'indicateurs</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indicateur_de_tendance_centrale&veaction=edit&section=1" title="Modifier la section : Exemples d'indicateurs" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Indicateur_de_tendance_centrale&action=edit&section=1" title="Modifier le code source de la section : Exemples d'indicateurs"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Les indicateurs suivants peuvent s'appliquer à des données unidimensionnelles. Selon les circonstances, il peut être approprié de transformer les données avant de calculer une tendance centrale, comme prendre les carrés ou les logarithmes des valeurs. Le choix de la transformation dépend fortement des données elles-mêmes. </p><p>On considère un échantillon de <i>n</i> valeurs <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},x_{2},\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> <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> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X=\{x_{1},x_{2},\ldots ,x_{n}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a91feefe12374bcabebcb922376817788fbd9f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.932ex; height:2.843ex;" alt="{\displaystyle X=\{x_{1},x_{2},\ldots ,x_{n}\}}"></span>, et sa version ordonnée <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 {\tilde {X}}=\{x_{(1)},x_{(2)},\ldots ,x_{(n)}\}}"> <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> <mo>=</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msub> <mo>,</mo> <mo>…<!-- … --></mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {X}}=\{x_{(1)},x_{(2)},\ldots ,x_{(n)}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09430be70e0d2893fd0f8475611848149b0ad468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:24.77ex; height:3.509ex;" alt="{\displaystyle {\tilde {X}}=\{x_{(1)},x_{(2)},\ldots ,x_{(n)}\}}"></span> </p> <dl><dt><a href="/wiki/Esp%C3%A9rance_math%C3%A9matique" title="Espérance mathématique">Espérance mathématique</a></dt> <dd>la <a href="/wiki/Moyenne_arithm%C3%A9tique" title="Moyenne arithmétique">moyenne arithmétique</a> de l'ensemble des données</dd> <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 \mathbb {E} (X)=\mathrm {A} (X)={\frac {1}{n}}\sum _{k=1}^{n}x_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">E</mi> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <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>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {E} (X)=\mathrm {A} (X)={\frac {1}{n}}\sum _{k=1}^{n}x_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70344d3bb4d6202e87591032aef77b2338a59e72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:25.847ex; height:6.843ex;" alt="{\displaystyle \mathbb {E} (X)=\mathrm {A} (X)={\frac {1}{n}}\sum _{k=1}^{n}x_{k}}"></span></dd> <dt><a href="/wiki/M%C3%A9diane_(statistiques)" title="Médiane (statistiques)">Médiane</a></dt> <dd>la valeur médiane qui sépare l'ensemble en deux, un ensemble où toutes les valeurs sont inférieures à la médiane et un deuxième où les valeurs lui sont supérieures. Avec le mode, la médiane sont les seules mesures de tendance centrale qui peuvent être utilisées pour des données ordonnées.</dd> <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 \mathrm {m} (X)={\begin{cases}x_{(p)}&\mathrm {si} \ n=2p+1\\{\frac {x_{(p)}+x_{(p+1)}}{2}}&\mathrm {si} \ n=2p\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mrow> </msub> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> </mrow> <mtext> </mtext> <mi>n</mi> <mo>=</mo> <mn>2</mn> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>+</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>p</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> </mrow> <mtext> </mtext> <mi>n</mi> <mo>=</mo> <mn>2</mn> <mi>p</mi> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {m} (X)={\begin{cases}x_{(p)}&\mathrm {si} \ n=2p+1\\{\frac {x_{(p)}+x_{(p+1)}}{2}}&\mathrm {si} \ n=2p\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d6da1b1e861eaa1a258d6393e5ddf43dec7f717" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:36.191ex; height:7.509ex;" alt="{\displaystyle \mathrm {m} (X)={\begin{cases}x_{(p)}&\mathrm {si} \ n=2p+1\\{\frac {x_{(p)}+x_{(p+1)}}{2}}&\mathrm {si} \ n=2p\end{cases}}}"></span></dd> <dt><a href="/wiki/Mode_(statistiques)" title="Mode (statistiques)">Mode</a></dt> <dd>la valeur la plus fréquente du jeu de données. C'est le seul indicateur de tendance centrale qui peut être utilisée sur des données nominales</dd> <dt><a href="/wiki/Moyenne_g%C3%A9n%C3%A9ralis%C3%A9e" class="mw-redirect" title="Moyenne généralisée">Moyenne généralisée</a></dt> <dd>Une généralisation des <a href="/wiki/Moyenne_pythagoricienne" title="Moyenne pythagoricienne">moyennes pythagoriciennes</a>, caractérisées par un exposant.</dd> <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 \mathrm {A} _{q}(X)={\sqrt[{q}]{{\frac {1}{n}}\sum _{k=1}^{n}x_{k}^{q}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <munderover> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</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>k</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msubsup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {A} _{q}(X)={\sqrt[{q}]{{\frac {1}{n}}\sum _{k=1}^{n}x_{k}^{q}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21b12d2b2a74b8aac2919466cf0a822ce86ed46b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:20.722ex; height:7.509ex;" alt="{\displaystyle \mathrm {A} _{q}(X)={\sqrt[{q}]{{\frac {1}{n}}\sum _{k=1}^{n}x_{k}^{q}}}}"></span></dd> <dt><a href="/wiki/Moyenne_g%C3%A9om%C3%A9trique" title="Moyenne géométrique">Moyenne géométrique</a></dt> <dd>la <a href="/wiki/Racine_d%27un_nombre" title="Racine d'un nombre">racine <i>n</i>-ième</a> du produit des données, pour un ensemble de <i>n</i> valeurs. Cette mesure ne fonctionne que si les données sont positives.</dd> <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 \mathrm {G} (X)={\sqrt[{n}]{\prod _{k=1}^{n}x_{k}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">G</mi> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mrow> <munderover> <mo>∏<!-- ∏ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {G} (X)={\sqrt[{n}]{\prod _{k=1}^{n}x_{k}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d4c0e20dbb942e041f245f32e709e8b4bfa50a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:16.811ex; height:7.509ex;" alt="{\displaystyle \mathrm {G} (X)={\sqrt[{n}]{\prod _{k=1}^{n}x_{k}}}}"></span></dd> <dt><a href="/wiki/Moyenne_harmonique" title="Moyenne harmonique">Moyenne harmonique</a></dt> <dd>l'<a href="/wiki/Inverse" title="Inverse">inverse</a> de la moyenne arithmétique des inverses des données. Cette mesure n'est valide que pour des valeurs strictement positives.</dd> <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 \mathrm {H} (X)={\frac {1}{{\frac {1}{n}}\sum _{k=1}^{n}{\frac {1}{x_{k}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <munderover> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mfrac> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {H} (X)={\frac {1}{{\frac {1}{n}}\sum _{k=1}^{n}{\frac {1}{x_{k}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/388c5258e68406d20052f2ab3d4d71a1695f81e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:20.343ex; height:7.009ex;" alt="{\displaystyle \mathrm {H} (X)={\frac {1}{{\frac {1}{n}}\sum _{k=1}^{n}{\frac {1}{x_{k}}}}}}"></span></dd> <dt><a href="/wiki/Moyenne_pond%C3%A9r%C3%A9e" title="Moyenne pondérée">Moyenne arithmétique pondérée</a></dt> <dd>une moyenne arithmétique où chaque valeur se voit associer un poids.</dd> <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 \mathbb {E} (X)=\mathrm {A} (X)={\frac {\sum _{k=1}^{n}\omega _{k}x_{k}}{\sum _{k=1}^{n}\omega _{k}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">E</mi> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <munderover> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>ω<!-- ω --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> <mrow> <munderover> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>ω<!-- ω --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {E} (X)=\mathrm {A} (X)={\frac {\sum _{k=1}^{n}\omega _{k}x_{k}}{\sum _{k=1}^{n}\omega _{k}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ae1eae985071d94bcf29567c7cea864ee3f88f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:28.888ex; height:6.843ex;" alt="{\displaystyle \mathbb {E} (X)=\mathrm {A} (X)={\frac {\sum _{k=1}^{n}\omega _{k}x_{k}}{\sum _{k=1}^{n}\omega _{k}}}}"></span></dd> <dt><a href="/wiki/Moyenne_tronqu%C3%A9e" title="Moyenne tronquée">Moyenne tronquée</a></dt> <dd>la moyenne arithmétique de données dont une partie des données les plus faibles et les plus hautes ont été ignorées.</dd> <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 {1}{n-2m}}\sum _{k=m}^{n-m}x_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>n</mi> <mo>−<!-- − --></mo> <mn>2</mn> <mi>m</mi> </mrow> </mfrac> </mrow> <munderover> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mi>m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−<!-- − --></mo> <mi>m</mi> </mrow> </munderover> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{n-2m}}\sum _{k=m}^{n-m}x_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/517de9435b81095acfb2ef5c1e36c49eedc44939" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.174ex; height:7.176ex;" alt="{\displaystyle {\frac {1}{n-2m}}\sum _{k=m}^{n-m}x_{k}}"></span></dd> <dt><a href="/wiki/Moyenne_interquartile" title="Moyenne interquartile">Moyenne interquartile</a></dt> <dd>une moyenne tronquée sur les données contenues dans l'<a href="/wiki/%C3%89cart_interquartile" title="Écart interquartile">intervalle interquartile</a>.</dd> <dt><a href="/wiki/Milieu_de_gamme_(statistique)" title="Milieu de gamme (statistique)">Milieu de gamme</a></dt> <dd>la moyenne arithmétique du minimum et du maximum des valeurs.</dd> <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 {\min X+\max X}{2}}={\frac {x_{(1)}+x_{(n)}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo movablelimits="true" form="prefix">min</mo> <mi>X</mi> <mo>+</mo> <mo movablelimits="true" form="prefix">max</mo> <mi>X</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msub> <mo>+</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\min X+\max X}{2}}={\frac {x_{(1)}+x_{(n)}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25837f61ff594377befa3bcbdf338f298ec9b453" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:30.878ex; height:5.509ex;" alt="{\displaystyle {\frac {\min X+\max X}{2}}={\frac {x_{(1)}+x_{(n)}}{2}}}"></span></dd> <dt><a href="/w/index.php?title=Midhinge&action=edit&redlink=1" class="new" title="Midhinge (page inexistante)">Midhinge</a> <a href="https://en.wikipedia.org/wiki/Midhinge" class="extiw" title="en:Midhinge"><span class="indicateur-langue" title="Article en anglais : « Midhinge »">(en)</span></a></dt> <dd>la moyenne arithmétique des premier et troisième <a href="/wiki/Quartile" title="Quartile">quartiles</a></dd> <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 {Q1+Q3}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>Q</mi> <mn>1</mn> <mo>+</mo> <mi>Q</mi> <mn>3</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {Q1+Q3}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44bb77fd2e6b4cc6da8fa51ce0e8422c80d73eb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.678ex; height:5.343ex;" alt="{\displaystyle {\frac {Q1+Q3}{2}}}"></span></dd> <dt><a href="/wiki/Moyenne_quasi-arithm%C3%A9tique" title="Moyenne quasi-arithmétique">Moyenne quasi-arithmétique</a></dt> <dd>Une généralisation de la <a href="/wiki/Moyenne_g%C3%A9n%C3%A9ralis%C3%A9e" class="mw-redirect" title="Moyenne généralisée">moyenne généralisée</a>, caractérisée par une <a href="/wiki/Fonction_(math%C3%A9matiques)" title="Fonction (mathématiques)">fonction</a> <a href="/wiki/Continuit%C3%A9_(math%C3%A9matiques)" title="Continuité (mathématiques)">continue</a> <a href="/wiki/Injectivit%C3%A9" class="mw-redirect" title="Injectivité">injective</a>.</dd> <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 f^{-1}\left({\frac {1}{n}}\sum _{k=1}^{n}f(x_{k})\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <munderover> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mi>f</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f^{-1}\left({\frac {1}{n}}\sum _{k=1}^{n}f(x_{k})\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9492a1c3a617652999f2cb1ee7a5cc8193d74535" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:19.588ex; height:7.509ex;" alt="{\displaystyle f^{-1}\left({\frac {1}{n}}\sum _{k=1}^{n}f(x_{k})\right)}"></span></dd> <dt><a href="/wiki/Trimoyenne_de_Tukey" class="mw-redirect" title="Trimoyenne de Tukey">Trimoyenne de Tukey</a></dt> <dd>la moyenne arithmétique pondérée de la médiane et des deux quartiles.</dd> <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 {Q1+2Q2+Q3}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>Q</mi> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mi>Q</mi> <mn>2</mn> <mo>+</mo> <mi>Q</mi> <mn>3</mn> </mrow> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {Q1+2Q2+Q3}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d1595974501e2e3eff94dd12cb5fb2e1a5559ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.682ex; height:5.343ex;" alt="{\displaystyle {\frac {Q1+2Q2+Q3}{4}}}"></span></dd> <dt><a href="/wiki/Winsorisation" title="Winsorisation">Moyenne winsorisée</a></dt> <dd>une moyenne arithmétique dans laquelle les <a href="/wiki/Outlier" class="mw-redirect" title="Outlier">valeurs extrêmes</a> sont remplacées par des valeurs plus proches de la médiane.</dd></dl> <p>Ces indicateurs peuvent être appliquées à des données multi-dimensionnelles, mais les résultats peuvent ne pas être invariantes par rotation. </p> <dl><dt><a href="/wiki/M%C3%A9diane_g%C3%A9om%C3%A9trique" title="Médiane géométrique">Médiane géométrique</a></dt> <dd>le point minimisant la somme des distances à un ensemble de points. C'est un équivalent de la médiane pour des données unidimensionnelles mais n'est pas la médiane de chaque dimension indépendamment. Elle n'est pas invariante aux changements d'échelle selon les dimensions.</dd> <dt><a href="/wiki/Moyenne_quadratique" title="Moyenne quadratique">Moyenne quadratique</a></dt> <dd>utile en ingénierie, mais peu en statistiques, car l'indicateur n'est pas efficace en cas de présence de données négatives.</dd> <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 \mathrm {Q} (X)={\sqrt {{\frac {1}{n}}\sum _{k=1}^{n}x_{k}^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Q</mi> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <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>k</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>k</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Q} (X)={\sqrt {{\frac {1}{n}}\sum _{k=1}^{n}x_{k}^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4f5527097a2448ffb440649f53d4d123e1dd61c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:19.798ex; height:7.509ex;" alt="{\displaystyle \mathrm {Q} (X)={\sqrt {{\frac {1}{n}}\sum _{k=1}^{n}x_{k}^{2}}}}"></span></dd> <dt><a href="/w/index.php?title=Profondeur_simpliciale&action=edit&redlink=1" class="new" title="Profondeur simpliciale (page inexistante)">Profondeur simpliciale</a> <a href="https://en.wikipedia.org/wiki/Simplicial_depth" class="extiw" title="en:Simplicial depth"><span class="indicateur-langue" title="Article en anglais : « Simplicial depth »">(en)</span></a></dt> <dd>la probabilité qu'un <a href="/wiki/Simplexe" title="Simplexe">simplexe</a> choisi aléatoirement pour une distribution donnée contienne le centre donné</dd> <dt><a href="/w/index.php?title=M%C3%A9diane_de_Tukey&action=edit&redlink=1" class="new" title="Médiane de Tukey (page inexistante)">Médiane de Tukey</a></dt> <dd>un point ayant la propriété que tout demi-espace le contenant contienne aussi de nombreux points</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Voir_aussi">Voir aussi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indicateur_de_tendance_centrale&veaction=edit&section=2" title="Modifier la section : Voir aussi" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Indicateur_de_tendance_centrale&action=edit&section=2" title="Modifier le code source de la section : Voir aussi"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Indicateur_de_position" title="Indicateur de position">Indicateur de position</a></li> <li><a href="/wiki/Indicateur_de_dispersion" title="Indicateur de dispersion">Indicateur de dispersion</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes_et_références"><span id="Notes_et_r.C3.A9f.C3.A9rences"></span>Notes et références</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indicateur_de_tendance_centrale&veaction=edit&section=3" title="Modifier la section : Notes et références" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Indicateur_de_tendance_centrale&action=edit&section=3" title="Modifier le code source de la section : Notes et références"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> Cet article est partiellement ou en totalité issu de l’article de Wikipédia en anglais intitulé <span class="plainlinks">« <a class="external text" href="https://en.wikipedia.org/wiki/Central_tendency?oldid=1169314262">Central tendency</a> » <small>(<a class="external text" href="https://en.wikipedia.org/wiki/Central_tendency?action=history">voir la liste des auteurs</a>)</small></span>.</li></ul> <ul id="bandeau-portail" class="bandeau-portail"><li><span class="bandeau-portail-element"><span class="bandeau-portail-icone"><span class="noviewer" typeof="mw:File"><a href="/wiki/Portail:Probabilit%C3%A9s_et_statistiques" title="Portail des probabilités et de la statistique"><img alt="icône décorative" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Logo_proba_4.svg/31px-Logo_proba_4.svg.png" decoding="async" width="31" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Logo_proba_4.svg/47px-Logo_proba_4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Logo_proba_4.svg/62px-Logo_proba_4.svg.png 2x" data-file-width="150" data-file-height="116" /></a></span></span> <span class="bandeau-portail-texte"><a href="/wiki/Portail:Probabilit%C3%A9s_et_statistiques" title="Portail:Probabilités et statistiques">Portail des probabilités et de la statistique</a></span> </span></li> </ul> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐565d46677b‐zkdft Cached time: 20241128121411 Cache expiry: 2592000 Reduced expiry: false Complications: [] CPU time usage: 0.094 seconds Real time usage: 0.193 seconds Preprocessor visited node count: 378/1000000 Post‐expand include size: 5290/2097152 bytes Template argument size: 462/2097152 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