4-/ - Moozonian Search

${\begin{aligned}\sigma &={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}(x_{i}-{\overline {x}})^{2}}}\\&={\sqrt {{\frac {1}{4}}\sum _{i=1}^{4}(x_{i}-{\overline {x}})^{2}}}&(N=4)\\&={\sqrt {{\frac {1}{4}}\sum _{i=1}^{4}(x_{i}-7)^{2}}}&({\overline {x}}=7)\\&={\sqrt {{\frac {1}{4}}\left[(x_{1}-7)^{2}+(x_{2}-7)^{2}+(x_{3}-7)^{2}+(x_{4}-7)^{2}\right]}}\\&={\sqrt {{\frac {1}{4}}\left[(5-7)^{2}+(6-7)^{2}+(8-7)^{2}+(9-7)^{2}\right]}}\\&={\sqrt {{\frac {1}{4}}\left((-2)^{2}+(-1)^{2}+1^{2}+2^{2}\right)}}\\&={\sqrt {{\frac {1}{4}}\left(4+1+1+4\right)}}\\&={\sqrt {\frac {10}{4}}}\\&\approx 1.58114\,.\end{aligned}}$

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標準偏差 - 维基百科，自由的百科全书

${\begin{aligned}{\overline {x}}&={\frac {1}{4}}\sum _{i=1}^{4}x_{i}&(N=4)\\&={\frac {1}{4}}\left(x_{1}+x_{2}+x_{3}+x_{4}\right)\\&={\frac {1}{4}}\left(5+6+8+9\right)\\&=7.\end{aligned}}$

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標準偏差 - 维基百科，自由的百科全书

${\begin{array}{ll}(2-5)^{2}=(-3)^{2}=9&(5-5)^{2}=0^{2}=0\\(4-5)^{2}=(-1)^{2}=1&(5-5)^{2}=0^{2}=0\\(4-5)^{2}=(-1)^{2}=1&(7-5)^{2}=2^{2}=4\\(4-5)^{2}=(-1)^{2}=1&(9-5)^{2}=4^{2}=16\end{array}}$

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நியமவிலகல் - தமிழ் விக்கிப்பீடியா

${\begin{array}{ll}(2-5)^{2}=(-3)^{2}=9&(5-5)^{2}=0^{2}=0\\(4-5)^{2}=(-1)^{2}=1&(5-5)^{2}=0^{2}=0\\(4-5)^{2}=(-1)^{2}=1&(7-5)^{2}=2^{2}=4\\(4-5)^{2}=(-1)^{2}=1&(9-5)^{2}=4^{2}=16\end{array}}$

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मानक विचलन - विकिपीडिया

${\begin{array}{ll}(2-5)^{2}=(-3)^{2}=9\\(4-5)^{2}=(-1)^{2}=1\\(4-5)^{2}=(-1)^{2}=1\\(4-5)^{2}=(-1)^{2}=1\\(5-5)^{2}=0^{2}=0\\(5-5)^{2}=0^{2}=0\\(7-5)^{2}=2^{2}=4\\(9-5)^{2}=4^{2}=16\end{array}}$

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Standardhälve – Vikipeedia

${\begin{array}{lll}(2-5)^{2}=(-3)^{2}=9&&(5-5)^{2}=0^{2}=0\\(4-5)^{2}=(-1)^{2}=1&&(5-5)^{2}=0^{2}=0\\(4-5)^{2}=(-1)^{2}=1&&(7-5)^{2}=2^{2}=4\\(4-5)^{2}=(-1)^{2}=1&&(9-5)^{2}=4^{2}=16\end{array}}$

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Desviació tipus - Viquipèdia, l'enciclopèdia ll...

${\begin{array}{lll}(2-5)^{2}=(-3)^{2}=9&&(5-5)^{2}=0^{2}=0\\(4-5)^{2}=(-1)^{2}=1&&(5-5)^{2}=0^{2}=0\\(4-5)^{2}=(-1)^{2}=1&&(7-5)^{2}=2^{2}=4\\(4-5)^{2}=(-1)^{2}=1&&(9-5)^{2}=4^{2}=16\\\end{array}}$

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Desviación típica - Wikipedia, la enciclopedia ...

${\begin{array}{lll}(2-5)^{2}=(-3)^{2}=9&&(5-5)^{2}=0^{2}=0\\(4-5)^{2}=(-1)^{2}=1&&(5-5)^{2}=0^{2}=0\\(4-5)^{2}=(-1)^{2}=1&&(7-5)^{2}=2^{2}=4\\(4-5)^{2}=(-1)^{2}=1&&(9-5)^{2}=4^{2}=16.\\\end{array}}$

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Standard deviation - Wikipedia

$m_{1}=\mathbb {E} [X]=\mu ,\quad m_{2}=\mathbb {E} [X^{2}]=\sigma ^{2}+\mu ^{2},\quad m_{3}=\mathbb {E} [X^{3}]=3\mu \sigma ^{2}+\mu ^{3},\quad m_{4}=\mathbb {E} [X^{4}]=3\sigma ^{4}+6\sigma ^{2}\mu ^{2}+\mu ^{4}$