@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: a skos:ConceptScheme .
psr:-TFZMWH4D-R
  skos:prefLabel "Pythagorean means"@en, "moyenne pythagoricienne"@fr ;
  a skos:Concept ;
  skos:narrower psr:-LBHHRTB4-0 .

psr:-LBHHRTB4-0
  skos:exactMatch <https://fr.wikipedia.org/wiki/Moyenne_harmonique>, <https://en.wikipedia.org/wiki/Harmonic_mean> ;
  skos:broader psr:-TFZMWH4D-R ;
  skos:inScheme psr: ;
  skos:definition """In mathematics, the <b>harmonic mean</b> is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired. The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, and 4 is  <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({\\rac {1^{-1}+4^{-1}+4^{-1}}{3}}\\
ight)^{-1}={\\rac {3}{{\\rac {1}{1}}+{\\rac {1}{4}}+{\\rac {1}{4}}}}={\\rac {3}{1.5}}=2\\\\,.}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mrow>             <mo>(</mo>             <mrow class="MJX-TeXAtom-ORD">               <mfrac>                 <mrow>                   <msup>                     <mn>1</mn>                     <mrow class="MJX-TeXAtom-ORD">                       <mo>−<!-- − --></mo>                       <mn>1</mn>                     </mrow>                   </msup>                   <mo>+</mo>                   <msup>                     <mn>4</mn>                     <mrow class="MJX-TeXAtom-ORD">                       <mo>−<!-- − --></mo>                       <mn>1</mn>                     </mrow>                   </msup>                   <mo>+</mo>                   <msup>                     <mn>4</mn>                     <mrow class="MJX-TeXAtom-ORD">                       <mo>−<!-- − --></mo>                       <mn>1</mn>                     </mrow>                   </msup>                 </mrow>                 <mn>3</mn>               </mfrac>             </mrow>             <mo>)</mo>           </mrow>           <mrow class="MJX-TeXAtom-ORD">             <mo>−<!-- − --></mo>             <mn>1</mn>           </mrow>         </msup>         <mo>=</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>3</mn>             <mrow>               <mrow class="MJX-TeXAtom-ORD">                 <mfrac>                   <mn>1</mn>                   <mn>1</mn>                 </mfrac>               </mrow>               <mo>+</mo>               <mrow class="MJX-TeXAtom-ORD">                 <mfrac>                   <mn>1</mn>                   <mn>4</mn>                 </mfrac>               </mrow>               <mo>+</mo>               <mrow class="MJX-TeXAtom-ORD">                 <mfrac>                   <mn>1</mn>                   <mn>4</mn>                 </mfrac>               </mrow>             </mrow>           </mfrac>         </mrow>         <mo>=</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>3</mn>             <mn>1.5</mn>           </mfrac>         </mrow>         <mo>=</mo>         <mn>2</mn>         <mspace width="thinmathspace"></mspace>         <mo>.</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\left({\\rac {1^{-1}+4^{-1}+4^{-1}}{3}}\\
ight)^{-1}={\\rac {3}{{\\rac {1}{1}}+{\\rac {1}{4}}+{\\rac {1}{4}}}}={\\rac {3}{1.5}}=2\\\\,.}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eca5906ddf61080e790c0d4df33f47e12da7d019" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:49.548ex; height:7.676ex;" alt="{\\\\displaystyle \\\\left({\\rac {1^{-1}+4^{-1}+4^{-1}}{3}}\\
ight)^{-1}={\\rac {3}{{\\rac {1}{1}}+{\\rac {1}{4}}+{\\rac {1}{4}}}}={\\rac {3}{1.5}}=2\\\\,.}"> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Harmonic_mean">https://en.wikipedia.org/wiki/Harmonic_mean</a>)"""@en, """La <b>moyenne harmonique</b> <span class="texhtml"><i>H</i></span> de nombres réels strictement positifs <span class="texhtml"><i>a</i><sub>1</sub>, ..., <i>a<sub>n</sub></i></span> est définie par :  <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 H={\\rac {n}{{\\\\dfrac {1}{a_{1}}}+{\\\\dfrac {1}{a_{2}}}+\\\\cdots +{\\\\dfrac {1}{a_{n}}}}}\\\\cdot }">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>H</mi>         <mo>=</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mi>n</mi>             <mrow>               <mrow class="MJX-TeXAtom-ORD">                 <mstyle displaystyle="true" scriptlevel="0">                   <mfrac>                     <mn>1</mn>                     <msub>                       <mi>a</mi>                       <mrow class="MJX-TeXAtom-ORD">                         <mn>1</mn>                       </mrow>                     </msub>                   </mfrac>                 </mstyle>               </mrow>               <mo>+</mo>               <mrow class="MJX-TeXAtom-ORD">                 <mstyle displaystyle="true" scriptlevel="0">                   <mfrac>                     <mn>1</mn>                     <msub>                       <mi>a</mi>                       <mrow class="MJX-TeXAtom-ORD">                         <mn>2</mn>                       </mrow>                     </msub>                   </mfrac>                 </mstyle>               </mrow>               <mo>+</mo>               <mo>⋯<!-- ⋯ --></mo>               <mo>+</mo>               <mrow class="MJX-TeXAtom-ORD">                 <mstyle displaystyle="true" scriptlevel="0">                   <mfrac>                     <mn>1</mn>                     <msub>                       <mi>a</mi>                       <mrow class="MJX-TeXAtom-ORD">                         <mi>n</mi>                       </mrow>                     </msub>                   </mfrac>                 </mstyle>               </mrow>             </mrow>           </mfrac>         </mrow>         <mo>⋅<!-- ⋅ --></mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle H={\\rac {n}{{\\\\dfrac {1}{a_{1}}}+{\\\\dfrac {1}{a_{2}}}+\\\\cdots +{\\\\dfrac {1}{a_{n}}}}}\\\\cdot }</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/534e42d67e1c1e9250834d4d0f49551fd8d72d49" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -5.338ex; width:27.414ex; height:8.176ex;" alt="{\\\\displaystyle H={\\rac {n}{{\\\\dfrac {1}{a_{1}}}+{\\\\dfrac {1}{a_{2}}}+\\\\cdots +{\\\\dfrac {1}{a_{n}}}}}\\\\cdot }"></span></dd></dl> C'est l'inverse de la moyenne arithmétique des inverses des termes. La moyenne harmonique est donc utilisée lorsqu'on veut déterminer un rapport moyen, dans un domaine où il existe des liens de proportionnalité inverses.  
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Moyenne_harmonique">https://fr.wikipedia.org/wiki/Moyenne_harmonique</a>)"""@fr ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:prefLabel "harmonic mean"@en, "moyenne harmonique"@fr ;
  a skos:Concept .