# What is the variance of {15, 14, 13, 13, 12, 10, 7}?

Nov 1, 2015

Variance of the data set is $6.29$.

#### Explanation:

Note that the formula of variance for calculation purpose is

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

where $n$ is the total number of values in the given data set.
In your given data we have $n = 7$ and the values of ${x}_{i}$'s are $\left\{15 , 14 , 13 , 13 , 12 , 10 , 7\right\}$ .

So, your variance $= \frac{1}{7} \left[{15}^{2} + {14}^{2} + {13}^{2} + {13}^{2} + {12}^{2} + {10}^{2} + {7}^{2}\right] - {\left(\frac{1}{7} \cdot \left[15 + 14 + 13 + 13 + 12 + 10 + 7\right]\right)}^{2}$
$= 150. 29 - 144$
$= 6.29$