Jump to navigation Jump to search

General

Display information for equation id:math.233307.1 on revision:233307

* Page found: Ancillary statistic (eq math.233307.1)

(force rerendering)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: c412a43c2f9e469c62a685b6c53dc629

TeX (original user input):

\hat{\sigma}^2:=\,\frac{\sum \left(X_i-\overline{X}\right)^2}{n}

TeX (checked):

{\hat {\sigma }}^{2}:=\,{\frac {\sum \left(X_{i}-{\overline {X}}\right)^{2}}{n}}

LaTeXML (experimental; uses MathML) rendering

MathML (4.625 KB / 1020 B) :

σ ^ 2 := ( X i - X ¯ ) 2 n assign superscript ^ 𝜎 2 superscript subscript 𝑋 𝑖 ¯ 𝑋 2 𝑛 {\displaystyle{\hat{\sigma}}^{2}:=\,{\frac{\sum\left(X_{i}-{\overline{X}}% \right)^{2}}{n}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\hat{\sigma}}^{2}:=\,{\frac{\sum\left(X_{i}-{\overline{X}}%&#10;\right)^{2}}{n}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">
      <msup id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">
        <mover accent="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
          <mi id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">σ</mi>
          <mo stretchy="false" id="p1.1.m1.1.1.1" xref="p1.1.m1.1.1.1.cmml">^</mo>
        </mover>
        <mn id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">2</mn>
      </msup>
      <mo rspace="4.2pt" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">:=</mo>
      <mstyle displaystyle="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
        <mfrac id="p1.1.m1.1.6a" xref="p1.1.m1.1.6.cmml">
          <mrow id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">
            <mo largeop="true" symmetric="true" id="p1.1.m1.1.6.2.1" xref="p1.1.m1.1.6.2.1.cmml"></mo>
            <msup id="p1.1.m1.1.6.2.9" xref="p1.1.m1.1.6.2.9.cmml">
              <mrow id="p1.1.m1.1.6.2.9.2" xref="p1.1.m1.1.6.2.9.2.2.cmml">
                <mo id="p1.1.m1.1.6.2.2" xref="p1.1.m1.1.6.2.9.2.2.cmml">(</mo>
                <mrow id="p1.1.m1.1.6.2.9.2.2" xref="p1.1.m1.1.6.2.9.2.2.cmml">
                  <msub id="p1.1.m1.1.6.2.9.2.2.1" xref="p1.1.m1.1.6.2.9.2.2.1.cmml">
                    <mi id="p1.1.m1.1.6.2.3" xref="p1.1.m1.1.6.2.3.cmml">X</mi>
                    <mi id="p1.1.m1.1.6.2.4.1" xref="p1.1.m1.1.6.2.4.1.cmml">i</mi>
                  </msub>
                  <mo id="p1.1.m1.1.6.2.5" xref="p1.1.m1.1.6.2.5.cmml">-</mo>
                  <mover accent="true" id="p1.1.m1.1.6.2.6" xref="p1.1.m1.1.6.2.6.cmml">
                    <mi id="p1.1.m1.1.6.2.6.2" xref="p1.1.m1.1.6.2.6.2.cmml">X</mi>
                    <mo id="p1.1.m1.1.6.2.6.1" xref="p1.1.m1.1.6.2.6.1.cmml">¯</mo>
                  </mover>
                </mrow>
                <mo id="p1.1.m1.1.6.2.7" xref="p1.1.m1.1.6.2.9.2.2.cmml">)</mo>
              </mrow>
              <mn id="p1.1.m1.1.6.2.8.1" xref="p1.1.m1.1.6.2.8.1.cmml">2</mn>
            </msup>
          </mrow>
          <mi id="p1.1.m1.1.6.3" xref="p1.1.m1.1.6.3.cmml">n</mi>
        </mfrac>
      </mstyle>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">
        <csymbol cd="latexml" id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">assign</csymbol>
        <apply id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">
          <csymbol cd="ambiguous" id="p1.1.m1.1.7.1.1.cmml" xref="p1.1.m1.1.7.1">superscript</csymbol>
          <apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
            <ci id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1.1">^</ci>
            <ci id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">𝜎</ci>
          </apply>
          <cn type="integer" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">2</cn>
        </apply>
        <apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
          <divide id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6"/>
          <apply id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">
            <sum id="p1.1.m1.1.6.2.1.cmml" xref="p1.1.m1.1.6.2.1"/>
            <apply id="p1.1.m1.1.6.2.9.cmml" xref="p1.1.m1.1.6.2.9">
              <csymbol cd="ambiguous" id="p1.1.m1.1.6.2.9.1.cmml" xref="p1.1.m1.1.6.2.9">superscript</csymbol>
              <apply id="p1.1.m1.1.6.2.9.2.2.cmml" xref="p1.1.m1.1.6.2.9.2">
                <minus id="p1.1.m1.1.6.2.5.cmml" xref="p1.1.m1.1.6.2.5"/>
                <apply id="p1.1.m1.1.6.2.9.2.2.1.cmml" xref="p1.1.m1.1.6.2.9.2.2.1">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.6.2.9.2.2.1.1.cmml" xref="p1.1.m1.1.6.2.9.2.2.1">subscript</csymbol>
                  <ci id="p1.1.m1.1.6.2.3.cmml" xref="p1.1.m1.1.6.2.3">𝑋</ci>
                  <ci id="p1.1.m1.1.6.2.4.1.cmml" xref="p1.1.m1.1.6.2.4.1">𝑖</ci>
                </apply>
                <apply id="p1.1.m1.1.6.2.6.cmml" xref="p1.1.m1.1.6.2.6">
                  <ci id="p1.1.m1.1.6.2.6.1.cmml" xref="p1.1.m1.1.6.2.6.1">¯</ci>
                  <ci id="p1.1.m1.1.6.2.6.2.cmml" xref="p1.1.m1.1.6.2.6.2">𝑋</ci>
                </apply>
              </apply>
              <cn type="integer" id="p1.1.m1.1.6.2.8.1.cmml" xref="p1.1.m1.1.6.2.8.1">2</cn>
            </apply>
          </apply>
          <ci id="p1.1.m1.1.6.3.cmml" xref="p1.1.m1.1.6.3">𝑛</ci>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\hat{\sigma}}^{2}:=\,{\frac{\sum\left(X_{i}-{\overline{X}}%
\right)^{2}}{n}}}</annotation>
  </semantics>
</math>

SVG (8.844 KB / 3.417 KB) :

ModifyingAbove sigma With caret squared colon equals StartFraction sigma-summation left-parenthesis upper X Subscript i Baseline minus upper X overbar right-parenthesis squared Over n EndFraction

MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Accents are not supported. - Reason: No translation possible for given token

Translation to Mathematica

In Mathematica:

Accents are not supported. - Reason: No translation possible for given token

Similar pages

Calculated based on the variables occurring on the entire Ancillary statistic page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results