Jayleen Sanders

2022-01-28

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

Anabelle Miller

Beginner2022-01-29Added 12 answers

Explanation:

Variance of a sample is given by the following equation:

$\sigma}^{2}=\frac{\sum {(x-\stackrel{\u2015}{x})}^{2}}{n-1$

It can be rearranged to:

$\sigma}^{2}=\frac{\sum {x}^{2}-\frac{(\sum x)}{n}}{n-1$

$\sum \left({x}^{2}\right)={2}^{2}+{3}^{2}+{4}^{2}+{6}^{2}+{8}^{2}+{9}^{2}=210$

$\sum \left(x\right)=2+3+4+6+8+9=32$

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.

$\sigma =\sqrt{7.8666}=2.80475786$

Variance of a sample is given by the following equation:

It can be rearranged to:

n=6

Standard deviation is the square root of variance.