Question

find the variance 12,22,28,24,21,16,31,14​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{12,22,28,24,21,16,31,14}$

$\underline{\textsf{To find:}}$

$\textsf{The variance of the given data}$

$\underline{\textsf{Solution:}}$

$\textsf{First we find out mean of the given data}$

$\textsf{Mean,}\;\mathsf{\overline{x}=\dfrac{\sum\,x_i}{n}}$

$\textsf{Mean}\;\mathsf{\overline{x}=\dfrac{12+22+28+24+21+16+31+14}{8}}$

$\textsf{Mean}\;\mathsf{\overline{x}=\dfrac{168}{8}}$

$\textsf{Mean,}\;\mathsf{\overline{x}=21}$

$\textsf{Now,}$

$\textsf{Variance}\;\mathsf{=\dfrac{\sum\,(x_i-\overline{x})^2}{n}}$

$\textsf{Variance}$$\mathsf{=\dfrac{(12-21)^2+(22-21)^2+(28-21)^2+(24-21)^2+(21-21)^2+(16-21)^2+(31-21)^2}{8}}\\\mathsf{\dfrac{+(14-21)^2}{}}$

$\textsf{Variance}\;$$\mathsf{=\dfrac{(-9)^2+(1)^2+(7)^2+(3)^2+(0)^2+(-5)^2+(10)^2+(-7)^2}{8}}$

$\textsf{Variance}\;\mathsf{=\dfrac{81+1+49+9+25+100+49}{8}}$

$\textsf{Variance}\;\mathsf{=\dfrac{314}{8}}$

$\textsf{Variance}\;\mathsf{=39.25}$

$\underline{\textsf{Answer:}}$

$\textsf{The variance of the given data is 39.25}$

Find more:

Calculate variance of 6,80,10,12,14.​

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