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{\displaystyle \chi ^{2}={\frac {Ns^{2}}{\sigma ^{2}}}}
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標準偏差 - Wikipedia
{\displaystyle V[X]=\int _{-\infty }^{\infty }\!{\big (}x-E[X]{\big )}^{2}f(x)\,dx}
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標準偏差 - Wikipedia
{\displaystyle E[X]=\int _{-\infty }^{\infty }\!xf(x)\,dx}
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標準偏差 - Wikipedia
{\displaystyle f(x)\geq 0,\quad \int _{-\infty }^{\infty }\!f(x)\,dx=1}
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標準偏差 - Wikipedia
{\displaystyle \int _{x_{1}}^{x_{2}}\!f(x)\,dx}
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標準偏差 - Wikipedia
{\displaystyle V[X]=E{\Bigl [}{\bigl (}X-E[X]{\bigr )}^{2}{\Bigr ]}=\textstyle \sum \limits _{i=1}^{\infty }p_{i}{\bigl (}x_{i}-E[X]{\bigr )}^{2}=E[X^{2}]-(E[X])^{2}}
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標準偏差 - Wikipedia
{\displaystyle E[X]=\textstyle \sum \limits _{i=1}^{\infty }p_{i}x_{i}}
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標準偏差 - Wikipedia
{\displaystyle \textstyle \sum \limits _{i=1}^{\infty }p_{i}=1\quad (p_{i}\geq 0)}
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標準偏差 - Wikipedia
{\displaystyle D\approx {\sqrt {{\frac {1}{n-1.5}}\textstyle \sum \limits _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}}={\sqrt {{\dfrac {1}{n-1.5}}\textstyle \sum \limits _{i=1}^{n}{x_{i}}^{2}-{\dfrac {n}{n-1.5}}{\bar {x}}^{2}}}}
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標準偏差 - Wikipedia
{\displaystyle D={\sqrt {\frac {n-1}{2}}}{\frac {\Gamma \left({\frac {n-1}{2}}\right)}{\Gamma \left({\frac {n}{2}}\right)}}v}
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標準偏差 - Wikipedia
{\displaystyle v^{2}={\frac {1}{n-1}}\textstyle \sum \limits _{i=1}^{n}(x_{i}-{\bar {x}})^{2}={\dfrac {1}{n-1}}\sum \limits _{i=1}^{n}{x_{i}}^{2}-{\dfrac {n}{n-1}}{\bar {x}}^{2}}
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標準偏差 - Wikipedia
{\displaystyle E[s^{2}]={\frac {n-1}{n}}\sigma ^{2}}
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標準偏差 - Wikipedia
{\displaystyle s^{2}={\frac {1}{n}}\textstyle \sum \limits _{i=1}^{n}(x_{i}-{\bar {x}})^{2}={\dfrac {1}{n}}\sum \limits _{i=1}^{n}{x_{i}}^{2}-{\bar {x}}^{2}}
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標準偏差 - Wikipedia
{\displaystyle {\bar {x}}={\frac {1}{n}}\textstyle \sum \limits _{i=1}^{n}x_{i}}
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標準偏差 - Wikipedia
{\displaystyle \sigma ^{2}={\frac {1}{n}}\textstyle \sum \limits _{i=1}^{n}(x_{i}-{\overline {x}})^{2}={\dfrac {1}{n}}\sum \limits _{i=1}^{n}{x_{i}}^{2}-{\overline {x}}^{2}}
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標準偏差 - Wikipedia
{\displaystyle {\overline {x}}={\frac {1}{n}}\textstyle \sum \limits _{i=1}^{n}x_{i}}
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標準偏差 - Wikipedia
{\displaystyle s^{2}={\frac {1}{n}}\textstyle \sum \limits _{i=1}^{n}(x_{i}-{\overline {x}})^{2}}
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標準偏差 - Wikipedia
{\displaystyle ns^{2}=\textstyle \sum \limits _{i=1}^{n}(x_{i}-{\overline {x}})^{2}}
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{\displaystyle \|{\boldsymbol {x}}-{\overline {\boldsymbol {x}}}\|=\|(\pm s,\cdots ,\pm s)\|}
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{\displaystyle s={\sqrt {{\frac {1}{n}}\textstyle \sum \limits _{i=1}^{n}(x_{i}-{\overline {x}})^{2}}}}
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標準偏差 - Wikipedia