# What is the variance of 2, 9, 3, 2, 7, 7, 12?

Jan 28, 2017

$14. \overline{6}$

#### Explanation:

The formula for the variance of a data set is

${s}^{2} = \frac{1}{n - 1} {\sum}_{k = 1}^{n} {\left(x - \overline{x}\right)}_{k}^{2}$

in this case $n = 7$

and

$\overline{x} = \frac{1}{n} {\sum}_{k = 1}^{n} {x}_{k} = \frac{2 + 9 + 3 + 2 + 7 + 7 + 12}{7} = \frac{11 + 5 + 14 + 12}{7} = \frac{16 + 26}{7} = \frac{42}{7} = 6$

Then

${s}^{2} = \frac{1}{6} {\sum}_{k = 1}^{7} {\left(x - 6\right)}_{k}^{2} = \frac{{\left(- 4\right)}^{2} + {3}^{2} + {\left(- 3\right)}^{2} + {\left(- 4\right)}^{2} + {1}^{2} + {1}^{2} + {6}^{2}}{6} = \frac{16 + 9 + 9 + 16 + 2 + 36}{6} = \frac{32 + 18 + 2 + 36}{6} = \frac{88}{6} = \frac{44}{3} = 14. \overline{6}$