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Tillgänglig på 60 språk" > <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-60" 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">60 språk</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_%D9%87%D9%86%D8%AF%D8%B3%D9%8A" title="متوسط هندسي – arabiska" lang="ar" hreflang="ar" data-title="متوسط هندسي" data-language-autonym="العربية" data-language-local-name="arabiska" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/H%C9%99nd%C9%99si_orta" title="Həndəsi orta – azerbajdzjanska" lang="az" hreflang="az" data-title="Həndəsi orta" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdzjanska" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A7%81%E0%A6%A3%E0%A7%8B%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A6%B0_%E0%A6%97%E0%A6%A1%E0%A6%BC" title="গুণোত্তর গড় – bengali" lang="bn" hreflang="bn" data-title="গুণোত্তর গড়" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</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%B3%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%87%D0%BD%D0%B0%D0%B5" title="Сярэдняе геаметрычнае – belarusiska" lang="be" hreflang="be" data-title="Сярэдняе геаметрычнае" data-language-autonym="Беларуская" data-language-local-name="belarusiska" class="interlanguage-link-target"><span>Беларуская</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%B3%D0%B5%D0%B0%D0%BC%D1%8D%D1%82%D1%80%D1%8B%D1%87%D0%BD%D0%B0%D0%B5" title="Сярэдняе геамэтрычнае – belarusiska (tarasjkevitsa)" lang="be-tarask" hreflang="be-tarask" data-title="Сярэдняе геамэтрычнае" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="belarusiska (tarasjkevitsa)" 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%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%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="Средногеометрична стойност – bulgariska" lang="bg" hreflang="bg" data-title="Средногеометрична стойност" data-language-autonym="Български" data-language-local-name="bulgariska" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Geometrijska_sredina" title="Geometrijska sredina – bosniska" lang="bs" hreflang="bs" data-title="Geometrijska sredina" data-language-autonym="Bosanski" data-language-local-name="bosniska" 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_geom%C3%A8trica" title="Mitjana geomètrica – katalanska" lang="ca" hreflang="ca" data-title="Mitjana geomètrica" data-language-autonym="Català" data-language-local-name="katalanska" 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%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D0%BB%D0%BB%D0%B5_%D0%B2%C4%83%D1%82%D0%B0%D0%BC%D0%BC%D0%B8" title="Геометрилле вăтамми – tjuvasjiska" lang="cv" hreflang="cv" data-title="Геометрилле вăтамми" data-language-autonym="Чӑвашла" data-language-local-name="tjuvasjiska" 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/Geometrick%C3%BD_pr%C5%AFm%C4%9Br" title="Geometrický průměr – tjeckiska" lang="cs" hreflang="cs" data-title="Geometrický průměr" data-language-autonym="Čeština" data-language-local-name="tjeckiska" 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/Geometrisk_gennemsnit" title="Geometrisk gennemsnit – danska" lang="da" hreflang="da" data-title="Geometrisk gennemsnit" data-language-autonym="Dansk" data-language-local-name="danska" 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/Geometrisches_Mittel" title="Geometrisches Mittel – tyska" lang="de" hreflang="de" data-title="Geometrisches Mittel" data-language-autonym="Deutsch" data-language-local-name="tyska" 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/Geomeetriline_keskmine" title="Geomeetriline keskmine – estniska" lang="et" hreflang="et" data-title="Geomeetriline keskmine" data-language-autonym="Eesti" data-language-local-name="estniska" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%B9%CE%BA%CF%8C%CF%82_%CE%BC%CE%AD%CF%83%CE%BF%CF%82" title="Γεωμετρικός μέσος – grekiska" lang="el" hreflang="el" data-title="Γεωμετρικός μέσος" data-language-autonym="Ελληνικά" data-language-local-name="grekiska" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Geometric_mean" title="Geometric mean – engelska" lang="en" hreflang="en" data-title="Geometric mean" data-language-autonym="English" data-language-local-name="engelska" 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_geom%C3%A9trica" title="Media geométrica – spanska" lang="es" hreflang="es" data-title="Media geométrica" data-language-autonym="Español" data-language-local-name="spanska" 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/Geometria_meznombro" title="Geometria meznombro – esperanto" lang="eo" hreflang="eo" data-title="Geometria meznombro" data-language-autonym="Esperanto" data-language-local-name="esperanto" 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_geometriko" title="Batezbesteko geometriko – baskiska" lang="eu" hreflang="eu" data-title="Batezbesteko geometriko" data-language-autonym="Euskara" data-language-local-name="baskiska" 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_%D9%87%D9%86%D8%AF%D8%B3%DB%8C" title="میانگین هندسی – persiska" lang="fa" hreflang="fa" data-title="میانگین هندسی" data-language-autonym="فارسی" data-language-local-name="persiska" 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_g%C3%A9om%C3%A9trique" title="Moyenne géométrique – franska" lang="fr" hreflang="fr" data-title="Moyenne géométrique" data-language-autonym="Français" data-language-local-name="franska" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Media_xeom%C3%A9trica" title="Media xeométrica – galiciska" lang="gl" hreflang="gl" data-title="Media xeométrica" data-language-autonym="Galego" data-language-local-name="galiciska" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B8%B0%ED%95%98_%ED%8F%89%EA%B7%A0" title="기하 평균 – koreanska" lang="ko" hreflang="ko" data-title="기하 평균" data-language-autonym="한국어" data-language-local-name="koreanska" class="interlanguage-link-target"><span>한국어</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%A5%D6%80%D5%AF%D6%80%D5%A1%D5%B9%D5%A1%D6%83%D5%A1%D5%AF%D5%A1%D5%B6" title="Միջին երկրաչափական – armeniska" lang="hy" hreflang="hy" data-title="Միջին երկրաչափական" data-language-autonym="Հայերեն" data-language-local-name="armeniska" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%97%E0%A5%81%E0%A4%A3%E0%A5%8B%E0%A4%A4%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="गुणोत्तर माध्य – hindi" lang="hi" hreflang="hi" data-title="गुणोत्तर माध्य" data-language-autonym="हिन्दी" data-language-local-name="hindi" 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/Geometrijska_sredina" title="Geometrijska sredina – kroatiska" lang="hr" hreflang="hr" data-title="Geometrijska sredina" data-language-autonym="Hrvatski" data-language-local-name="kroatiska" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Rata-rata_geometrik" title="Rata-rata geometrik – indonesiska" lang="id" hreflang="id" data-title="Rata-rata geometrik" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiska" class="interlanguage-link-target"><span>Bahasa Indonesia</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%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99" title="ממוצע גאומטרי – hebreiska" lang="he" hreflang="he" data-title="ממוצע גאומטרי" data-language-autonym="עברית" data-language-local-name="hebreiska" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D0%BB%D1%8B%D2%9B_%D0%BE%D1%80%D1%82%D0%B0_%D1%88%D0%B0%D0%BC%D0%B0" title="Геометриялық орта шама – kazakiska" lang="kk" hreflang="kk" data-title="Геометриялық орта шама" data-language-autonym="Қазақша" data-language-local-name="kazakiska" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Valor_medius_geometricus" title="Valor medius geometricus – latin" lang="la" hreflang="la" data-title="Valor medius geometricus" data-language-autonym="Latina" data-language-local-name="latin" 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/%C4%A2eometriskais_vid%C4%93jais" title="Ģeometriskais vidējais – lettiska" lang="lv" hreflang="lv" data-title="Ģeometriskais vidējais" data-language-autonym="Latviešu" data-language-local-name="lettiska" 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/Geometrinis_vidurkis" title="Geometrinis vidurkis – litauiska" lang="lt" hreflang="lt" data-title="Geometrinis vidurkis" data-language-autonym="Lietuvių" data-language-local-name="litauiska" 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/M%C3%A9rtani_k%C3%B6z%C3%A9p" title="Mértani közép – ungerska" lang="hu" hreflang="hu" data-title="Mértani közép" data-language-autonym="Magyar" data-language-local-name="ungerska" 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%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%81%D0%BA%D0%B0_%D1%81%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D0%B0" title="Геометриска средина – makedonska" lang="mk" hreflang="mk" data-title="Геометриска средина" data-language-autonym="Македонски" data-language-local-name="makedonska" 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/Meetkundig_gemiddelde" title="Meetkundig gemiddelde – nederländska" lang="nl" hreflang="nl" data-title="Meetkundig gemiddelde" data-language-autonym="Nederlands" data-language-local-name="nederländska" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%B9%BE%E4%BD%95%E5%B9%B3%E5%9D%87" title="幾何平均 – japanska" lang="ja" hreflang="ja" data-title="幾何平均" data-language-autonym="日本語" data-language-local-name="japanska" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Geometrisk_gjennomsnitt" title="Geometrisk gjennomsnitt – norskt bokmål" lang="nb" hreflang="nb" data-title="Geometrisk gjennomsnitt" data-language-autonym="Norsk bokmål" data-language-local-name="norskt bokmål" 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/Geometrisk_middel" title="Geometrisk middel – nynorska" lang="nn" hreflang="nn" data-title="Geometrisk middel" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorska" 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/Geometrik_o%CA%BBrta" title="Geometrik oʻrta – uzbekiska" lang="uz" hreflang="uz" data-title="Geometrik oʻrta" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbekiska" 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_geom%C3%A9trica" title="Media geométrica – piemontesiska" lang="pms" hreflang="pms" data-title="Media geométrica" data-language-autonym="Piemontèis" data-language-local-name="piemontesiska" 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_geometryczna" title="Średnia geometryczna – polska" lang="pl" hreflang="pl" data-title="Średnia geometryczna" data-language-autonym="Polski" data-language-local-name="polska" 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_geom%C3%A9trica" title="Média geométrica – portugisiska" lang="pt" hreflang="pt" data-title="Média geométrica" data-language-autonym="Português" data-language-local-name="portugisiska" 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_geometric%C4%83" title="Medie geometrică – rumänska" lang="ro" hreflang="ro" data-title="Medie geometrică" data-language-autonym="Română" data-language-local-name="rumänska" 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%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5" title="Среднее геометрическое – ryska" lang="ru" hreflang="ru" data-title="Среднее геометрическое" data-language-autonym="Русский" data-language-local-name="ryska" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Mesatarja_gjeometrike" title="Mesatarja gjeometrike – albanska" lang="sq" hreflang="sq" data-title="Mesatarja gjeometrike" data-language-autonym="Shqip" data-language-local-name="albanska" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Geometric_mean" title="Geometric mean – Simple English" lang="en-simple" hreflang="en-simple" data-title="Geometric mean" 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/Geometrick%C3%BD_priemer" title="Geometrický priemer – slovakiska" lang="sk" hreflang="sk" data-title="Geometrický priemer" data-language-autonym="Slovenčina" data-language-local-name="slovakiska" 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/Geometri%C4%8Dna_sredina" title="Geometrična sredina – slovenska" lang="sl" hreflang="sl" data-title="Geometrična sredina" data-language-autonym="Slovenščina" data-language-local-name="slovenska" 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_%D8%A6%DB%95%D9%86%D8%AF%D8%A7%D8%B2%DB%95%DB%8C%DB%8C" title="ناوەندی ئەندازەیی – centralkurdiska" lang="ckb" hreflang="ckb" data-title="ناوەندی ئەندازەیی" data-language-autonym="کوردی" data-language-local-name="centralkurdiska" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Geometrijska_sredina" title="Geometrijska sredina – serbiska" lang="sr" hreflang="sr" data-title="Geometrijska sredina" data-language-autonym="Српски / srpski" data-language-local-name="serbiska" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Geometrijska_sredina" title="Geometrijska sredina – serbokroatiska" lang="sh" hreflang="sh" data-title="Geometrijska sredina" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatiska" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Geometrinen_keskiarvo" title="Geometrinen keskiarvo – finska" lang="fi" hreflang="fi" data-title="Geometrinen keskiarvo" data-language-autonym="Suomi" data-language-local-name="finska" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AF%86%E0%AE%B0%E0%AF%81%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%B2%E0%AF%8D_%E0%AE%9A%E0%AE%B0%E0%AE%BE%E0%AE%9A%E0%AE%B0%E0%AE%BF" title="பெருக்கல் சராசரி – tamil" lang="ta" hreflang="ta" data-title="பெருக்கல் சராசரி" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</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%A3%E0%B8%82%E0%B8%B2%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95" title="มัชฌิมเรขาคณิต – thailändska" lang="th" hreflang="th" data-title="มัชฌิมเรขาคณิต" data-language-autonym="ไทย" data-language-local-name="thailändska" 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/Geometrik_ortalama" title="Geometrik ortalama – turkiska" lang="tr" hreflang="tr" data-title="Geometrik ortalama" data-language-autonym="Türkçe" data-language-local-name="turkiska" 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%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B5" title="Середнє геометричне – ukrainska" lang="uk" hreflang="uk" data-title="Середнє геометричне" data-language-autonym="Українська" data-language-local-name="ukrainska" 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/%DB%81%D9%86%D8%AF%D8%B3%DB%8C_%D8%A7%D9%88%D8%B3%D8%B7" title="ہندسی اوسط – urdu" lang="ur" hreflang="ur" data-title="ہندسی 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/Trung_b%C3%ACnh_nh%C3%A2n" title="Trung bình nhân – vietnamesiska" lang="vi" hreflang="vi" data-title="Trung bình nhân" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesiska" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%87%A0%E4%BD%95%E5%B9%B3%E5%9D%87%E6%95%B0" title="几何平均数 – wu" lang="wuu" hreflang="wuu" data-title="几何平均数" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%B9%BE%E4%BD%95%E5%B9%B3%E5%9D%87%E5%80%BC" title="幾何平均值 – kantonesiska" lang="yue" hreflang="yue" data-title="幾何平均值" data-language-autonym="粵語" data-language-local-name="kantonesiska" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%87%A0%E4%BD%95%E5%B9%B3%E5%9D%87%E6%95%B0" title="几何平均数 – kinesiska" lang="zh" hreflang="zh" data-title="几何平均数" data-language-autonym="中文" data-language-local-name="kinesiska" class="interlanguage-link-target"><span>中文</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/Q185049#sitelinks-wikipedia" title="Redigera interwikilänkar" class="wbc-editpage">Redigera länkar</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div 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#c0c090;background-color:#f8eaba}.mw-parser-output .messagebox.nested-talk{border:1px solid #c0c090;background-color:#f8eaba;width:100%;margin:2px 4px}</style><table class="metadata ambox ambox-content" style=""> <tbody><tr> <td class="ambox-image"> <div style="width:52px;"><span typeof="mw:File"><a href="/wiki/Fil:Question_book-4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/40px-Question_book-4.svg.png" decoding="async" width="40" height="31" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/60px-Question_book-4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/80px-Question_book-4.svg.png 2x" data-file-width="262" data-file-height="204" /></a></span></div></td> <td class="ambox-text">Den här artikeln <b>behöver <a href="/wiki/Wikipedia:K%C3%A4llh%C3%A4nvisningar" title="Wikipedia:Källhänvisningar">källhänvisningar</a> för att kunna <a href="/wiki/Wikipedia:Verifierbarhet" title="Wikipedia:Verifierbarhet">verifieras</a>.</b> <small>(2022-09)</small> <br /><small>Åtgärda genom att lägga till pålitliga källor (<a href="/wiki/Wikipedia:Introduktion_till_k%C3%A4llh%C3%A4nvisningar" title="Wikipedia:Introduktion till källhänvisningar">gärna som fotnoter</a>). Uppgifter utan källhänvisning kan <a href="/wiki/Mall:K%C3%A4lla_beh%C3%B6vs" title="Mall:Källa behövs">ifrågasättas</a> och tas bort utan att det behöver diskuteras på <a href="/w/index.php?title=Diskussion:Geometriskt_medelv%C3%A4rde&action=edit&redlink=1" class="new" title="Diskussion:Geometriskt medelvärde [inte skriven än]">diskussionssidan</a>.</small></td> </tr> </tbody></table> <p>Ett <b>geometriskt <a href="/wiki/Medelv%C3%A4rde" title="Medelvärde">medelvärde</a></b> av <i>n</i> positiva tal <i>a</i><sub>1</sub>,..., <i>a</i><sub>n</sub> beräknas enligt </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 {\tilde {a}}={\sqrt[{n}]{a_{1}\cdot a_{2}\cdot ...\cdot a_{n}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <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> <mo>.</mo> <mo>⋅</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {a}}={\sqrt[{n}]{a_{1}\cdot a_{2}\cdot ...\cdot a_{n}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/145e26ed1ef05ca33568dab5d5198836685f979c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:19.355ex; height:3.009ex;" alt="{\displaystyle {\tilde {a}}={\sqrt[{n}]{a_{1}\cdot a_{2}\cdot ...\cdot a_{n}}}}"></span></dd></dl> <p>Geometriskt medelvärde kan benämnas som <a href="/wiki/Rot_av_tal" title="Rot av tal">n:te roten</a> av talens <a href="/wiki/Produkt_(matematik)" title="Produkt (matematik)">produkt</a>. </p><p>Geometriskt medelvärde används exempelvis vid uträkning av den genomsnittliga räntan för ett antal år. </p><p>Det geometriska medelvärdet av <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_{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> <mo>.</mo> <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_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9bcc0e499b63bdf3e61e2769f2df6d70b2aff65" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.902ex; height:2.009ex;" alt="{\displaystyle a_{1},...,a_{n}}"></span> är mindre än eller lika med motsvarande <a href="/wiki/Aritmetiskt_medelv%C3%A4rde" title="Aritmetiskt medelvärde">aritmetiska medelvärde</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 {\tilde {a}}\leq {\bar {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mo>≤</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {a}}\leq {\bar {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ae993ed30f1b387f840c5d1baf87737c560e5ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.558ex; height:2.343ex;" alt="{\displaystyle {\tilde {a}}\leq {\bar {a}}}"></span>), vilket brukar kallas för AM-GM-olikheten. </p> <div class="mw-heading mw-heading2"><h2 id="Egenskaper">Egenskaper</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geometriskt_medelv%C3%A4rde&veaction=edit&section=1" title="Redigera avsnitt: Egenskaper" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Geometriskt_medelv%C3%A4rde&action=edit&section=1" title="Redigera avsnitts källkod: Egenskaper"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Den grundläggande egenskapen hos det geometriska medelvärdet, som inte gäller för något annat medelvärde, är att </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 GM\left({\frac {X_{i}}{Y_{i}}}\right)={\frac {GM(X_{i})}{GM(Y_{i})}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mi>M</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>G</mi> <mi>M</mi> <mo stretchy="false">(</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>G</mi> <mi>M</mi> <mo stretchy="false">(</mo> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle GM\left({\frac {X_{i}}{Y_{i}}}\right)={\frac {GM(X_{i})}{GM(Y_{i})}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08181ad273de4ff3c85a73808a60149cfd87424b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:24.374ex; height:6.509ex;" alt="{\displaystyle GM\left({\frac {X_{i}}{Y_{i}}}\right)={\frac {GM(X_{i})}{GM(Y_{i})}}}"></span></dd></dl> <p>Detta gör det geometriska medelvärdet det enda riktiga medelvärdet för <i>normaliserade</i> resultat, det vill säga resultat som presenteras som förhållanden till referensvärden. </p><p>Detta är till exempel fallet när datorers prestanda jämförs med avseende på en referensdator eller vid beräkning av ett enda medeltal från flera heterogena källor (exempelvis livslängd, utbildningsår och spädbarnsdödlighet). I dessa fall kan det aritmetiska eller harmoniska medelvärdet ändra rangordningen av de olika värdena beroende på vad som används som referens. Ta till exempel följande jämförelse av exekveringstid för datorprogram: </p> <table class="wikitable"> <tbody><tr> <th> </th> <th>Dator A</th> <th>Dator B</th> <th>Dator C </th></tr> <tr> <td><b>Program 1</b></td> <td>1</td> <td>10</td> <td>20 </td></tr> <tr> <td><b>Program 2</b></td> <td>1000</td> <td>100</td> <td>20 </td></tr> <tr> <td><b>Aritmetiskt medelvärde</b></td> <td>500,5</td> <td>55</td> <td><b>20</b> </td></tr> <tr> <td><b>Geometriskt medelvärde</b></td> <td>31,622</td> <td>31,622</td> <td><b>20</b> </td></tr></tbody></table> <p>Det aritmetiska och geometriska medelvärdet indikerar båda att datorn C är den snabbaste. Men genom att presentera på lämpligt sätt normaliserade värden <i>och</i> använda det aritmetiska medelvärdet, kan det visas att någon av de andra två datorerna är den snabbaste. Normalisering av A:s resultat ger A som den snabbaste datorn enligt det aritmetiska medelvärdet: </p> <table class="wikitable"> <tbody><tr> <th> </th> <th>Dator A</th> <th>Dator B</th> <th>Dator C </th></tr> <tr> <td><b>Program 1</b></td> <td>1</td> <td>10</td> <td>20 </td></tr> <tr> <td><b>Program 2</b></td> <td>1</td> <td>0,1</td> <td>0,02 </td></tr> <tr> <td><b>Aritmetiskt medelvärde</b></td> <td><b>1</b></td> <td>5,05</td> <td>10,01 </td></tr> <tr> <td><b>Geometriskt medelvärde</b></td> <td>1</td> <td>1</td> <td><b>0,632</b> </td></tr></tbody></table> <p>och att därefter normalisera B:s resultat ger B som den snabbaste datorn enligt det aritmetiska medelvärdet: </p> <table class="wikitable"> <tbody><tr> <th> </th> <th>Dator A</th> <th>Dator B</th> <th>Dator C </th></tr> <tr> <td><b>Program 1</b></td> <td>0,1</td> <td>1</td> <td>2 </td></tr> <tr> <td><b>Program 2</b></td> <td>10</td> <td>1</td> <td>0,2 </td></tr> <tr> <td><b>Aritmetiskt medelvärde</b></td> <td>5,05</td> <td><b>1</b></td> <td>1,1 </td></tr> <tr> <td><b>Geometriskt medelvärde</b></td> <td>1</td> <td>1</td> <td><b>0,632</b> </td></tr></tbody></table> <p>Det geometriska medelvärdets rangordningar förblir desamma som den rangordning som erhålls med icke normaliserade värden. </p> <div class="mw-heading mw-heading2"><h2 id="Jämförelse_med_andra_medelvärden"><span id="J.C3.A4mf.C3.B6relse_med_andra_medelv.C3.A4rden"></span>Jämförelse med andra medelvärden</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geometriskt_medelv%C3%A4rde&veaction=edit&section=2" title="Redigera avsnitt: Jämförelse med andra medelvärden" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Geometriskt_medelv%C3%A4rde&action=edit&section=2" title="Redigera avsnitts källkod: Jämförelse med andra medelvärden"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Mean-values-2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Mean-values-2.png/300px-Mean-values-2.png" decoding="async" width="300" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Mean-values-2.png/450px-Mean-values-2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Mean-values-2.png/600px-Mean-values-2.png 2x" data-file-width="807" data-file-height="483" /></a><figcaption>Geometrisk jämförelse av medelvärden</figcaption></figure><div style="clear:left;"></div> <p>Medelvärden av två tal, <i>a</i> och <i>b</i>, kan konstrueras geometriskt med hjälp av en halvcirkel med diametern <i>a</i> + <i>b</i>. </p> <dl><dd><i>A</i>: Aritmetiska medelvärdet</dd> <dd><i>Q</i>: Kvadratiska medelvärdet</dd> <dd><i>H</i>: Harmoniska medelvärdet</dd> <dd><i>G</i>: Geometriska medelvärdet</dd></dl> <p>Det framgår att </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 {\bar {a}}_{Q}\geq {\bar {a}}_{A}\geq {\bar {a}}_{G}\geq {\bar {a}}_{H}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> </mrow> </msub> <mo>≥</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>≥</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> </msub> <mo>≥</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {a}}_{Q}\geq {\bar {a}}_{A}\geq {\bar {a}}_{G}\geq {\bar {a}}_{H}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a2443db625bbbcd4ea71aa6d4af7eee816212f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.427ex; height:2.676ex;" alt="{\displaystyle {\bar {a}}_{Q}\geq {\bar {a}}_{A}\geq {\bar {a}}_{G}\geq {\bar {a}}_{H}}"></span></dd></dl> <p>Denna ordning gäller även för ett godtyckligt antal tal. </p> <style data-mw-deduplicate="TemplateStyles:r56287950">.mw-parser-output table.navbox{border:#aaa 1px solid;width:100%;margin:auto;margin-top:1em;clear:both;font-size:88%;text-align:center;padding:1px}.mw-parser-output link+table.navbox{margin-top:-1px}.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow,.mw-parser-output table.navbox th{text-align:center;padding-left:1em;padding-right:1em}.mw-parser-output .navbox-thlinkcolor .navbox-title button,.mw-parser-output .navbox-thlinkcolor .navbox-title .mw-collapsible-text,.mw-parser-output .navbox-thlinkcolor .navbox-title a{color:inherit}.mw-parser-output .nowraplinks a,.mw-parser-output .nowraplinks .selflink{white-space:nowrap}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right;font-weight:bold;padding-left:1em;padding-right:1em}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background:#fdfdfd}.mw-parser-output .navbox-list{border-color:#fdfdfd}.mw-parser-output .navbox-title,.mw-parser-output table.navbox th{background:#b0c4de}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background:#d0e0f5}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background:#deeafa}.mw-parser-output .navbox-even{background:#f7f7f7}.mw-parser-output .navbox-odd{background:transparent}</style><table class="navbox" style="border-spacing:0; 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