Jayleen Sanders

2022-01-28

How do you find the variance and standard deviation of {2,3,4,6,8,9}?

Anabelle Miller

Explanation:
Variance of a sample is given by the following equation:
${\sigma }^{2}=\frac{\sum {\left(x-\stackrel{―}{x}\right)}^{2}}{n-1}$
It can be rearranged to:
${\sigma }^{2}=\frac{\sum {x}^{2}-\frac{\left(\sum x\right)}{n}}{n-1}$
$\sum \left({x}^{2}\right)={2}^{2}+{3}^{2}+{4}^{2}+{6}^{2}+{8}^{2}+{9}^{2}=210$
$\sum \left(x\right)=2+3+4+6+8+9=32$
n=6
${\sigma }^{2}=\frac{210-\left(\frac{{32}^{2}}{6}\right)}{6-1}=\frac{118}{15}\stackrel{\sim }{=}7.867$
Standard deviation is the square root of variance.
$\sigma =\sqrt{7.8666}=2.80475786$

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