@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-R9WD38J9-W
  skos:exactMatch <https://en.wikipedia.org/wiki/Geometric_mean>, <https://fr.wikipedia.org/wiki/Moyenne_g%C3%A9om%C3%A9trique> ;
  a skos:Concept ;
  skos:prefLabel "moyenne géométrique"@fr, "geometric mean"@en ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:related psr:-GN61B72S-G, psr:-F9XKFTD5-D ;
  skos:definition """En mathématiques, la moyenne géométrique est un type de moyenne. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Moyenne_g%C3%A9om%C3%A9trique">https://fr.wikipedia.org/wiki/Moyenne_g%C3%A9om%C3%A9trique</a>)"""@fr, """In mathematics, the <b>geometric mean</b> is a mean or average which indicates a central tendency of a finite set of real numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum).  The geometric mean is defined as the <span class="texhtml"><i>n</i></span>th root of the product of <span class="texhtml mvar" style="font-style:italic;">n</span> numbers, i.e., for a set of numbers <span class="texhtml"><i>a</i><sub>1</sub>, <i>a</i><sub>2</sub>, ..., <i>a<sub>n</sub></i></span>, the geometric mean is defined as  <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 \\\\left(\\\\prod _{i=1}^{n}a_{i}\\
ight)^{\\rac {1}{n}}={\\\\sqrt[{n}]{a_{1}a_{2}\\\\cdots a_{n}}}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mrow>             <mo>(</mo>             <mrow>               <munderover>                 <mo>∏<!-- ∏ --></mo>                 <mrow class="MJX-TeXAtom-ORD">                   <mi>i</mi>                   <mo>=</mo>                   <mn>1</mn>                 </mrow>                 <mrow class="MJX-TeXAtom-ORD">                   <mi>n</mi>                 </mrow>               </munderover>               <msub>                 <mi>a</mi>                 <mrow class="MJX-TeXAtom-ORD">                   <mi>i</mi>                 </mrow>               </msub>             </mrow>             <mo>)</mo>           </mrow>           <mrow class="MJX-TeXAtom-ORD">             <mfrac>               <mn>1</mn>               <mi>n</mi>             </mfrac>           </mrow>         </msup>         <mo>=</mo>         <mrow class="MJX-TeXAtom-ORD">           <mroot>             <mrow>               <msub>                 <mi>a</mi>                 <mrow class="MJX-TeXAtom-ORD">                   <mn>1</mn>                 </mrow>               </msub>               <msub>                 <mi>a</mi>                 <mrow class="MJX-TeXAtom-ORD">                   <mn>2</mn>                 </mrow>               </msub>               <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 \\\\left(\\\\prod _{i=1}^{n}a_{i}\\
ight)^{\\rac {1}{n}}={\\\\sqrt[{n}]{a_{1}a_{2}\\\\cdots a_{n}}}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8b67da21f4b58d3121ef21e0c5a9d040a6b65ce" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:26.485ex; height:8.676ex;" alt="{\\\\displaystyle \\\\left(\\\\prod _{i=1}^{n}a_{i}\\
ight)^{\\rac {1}{n}}={\\\\sqrt[{n}]{a_{1}a_{2}\\\\cdots a_{n}}}}"></span></dd></dl> or, equivalently, as the arithmetic mean in logscale:  <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 \\\\exp {\\\\left({{\\rac {1}{n}}\\\\sum \\\\limits _{i=1}^{n}\\\\ln a_{i}}\\
ight)}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>exp</mi>         <mo>⁡<!-- ⁡ --></mo>         <mrow class="MJX-TeXAtom-ORD">           <mrow>             <mo>(</mo>             <mrow class="MJX-TeXAtom-ORD">               <mrow class="MJX-TeXAtom-ORD">                 <mfrac>                   <mn>1</mn>                   <mi>n</mi>                 </mfrac>               </mrow>               <munderover>                 <mo movablelimits="false">∑<!-- ∑ --></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>               <mi>ln</mi>               <mo>⁡<!-- ⁡ --></mo>               <msub>                 <mi>a</mi>                 <mrow class="MJX-TeXAtom-ORD">                   <mi>i</mi>                 </mrow>               </msub>             </mrow>             <mo>)</mo>           </mrow>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\exp {\\\\left({{\\rac {1}{n}}\\\\sum \\\\limits _{i=1}^{n}\\\\ln a_{i}}\\
ight)}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ac879edd81a90120c557af2e05ef65669d83103" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:18.337ex; height:7.509ex;" alt="{\\\\displaystyle \\\\exp {\\\\left({{\\rac {1}{n}}\\\\sum \\\\limits _{i=1}^{n}\\\\ln a_{i}}\\
ight)}}"> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Geometric_mean">https://en.wikipedia.org/wiki/Geometric_mean</a>)"""@en ;
  skos:broader psr:-TFZMWH4D-R ;
  skos:inScheme psr: .

psr:-F9XKFTD5-D
  skos:prefLabel "inequality of arithmetic and geometric means"@en, "inégalité arithmético-géométrique"@fr ;
  a skos:Concept ;
  skos:related psr:-R9WD38J9-W .

psr:-GN61B72S-G
  skos:prefLabel "Maclaurin's inequality"@en, "inégalité de Maclaurin"@fr ;
  a skos:Concept ;
  skos:related psr:-R9WD38J9-W .

psr:-TFZMWH4D-R
  skos:prefLabel "Pythagorean means"@en, "moyenne pythagoricienne"@fr ;
  a skos:Concept ;
  skos:narrower psr:-R9WD38J9-W .

psr: a skos:ConceptScheme .