# How do you find the variance of the data 2,

How do you find the variance of the data 2, 4, 6, 8, 10?
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sainareon2
Explanation:
Variance $\left({\sigma }^{2}\right)$ is the average of squared difference from mean.
Mean is $M=\frac{2+4+6+8+10}{5}=\frac{30}{5}=6$
Variance is ${\sigma }^{2}=\frac{{\left(2-6\right)}^{2}+{\left(4-6\right)}^{2}+{\left(6-6\right)}^{2}+{\left(8-6\right)}^{2}+{\left(10-6\right)}^{2}}{5}$
$=\frac{16+4+0+16+4}{5}=\frac{40}{5}=8$
So the variance is 8 [Ans]
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search633504
Mean, $\stackrel{―}{x}=\frac{2+4+6+8+10}{5}=\frac{30}{5}=6$
$\therefore$ Variance $=\frac{1}{n}\sum {\left({x}_{i}-\stackrel{―}{x}\right)}^{2}$
$=\frac{1}{5}\le ft\left\{{\left(2-6\right)}^{2}+{\left(4-6\right)}^{2}+{\left(6-6\right)}^{2}+{\left(8-6\right)}^{2}+{\left(10-6\right)}^{2}right\right\}$
$=\frac{1}{5}\le ft\left\{16+4+0+4+16right\right\}=\frac{1}{5}×40=8$