# What is the variance of {15, 4, 2, -7, 8, 10}?

Mar 19, 2016

47.9

#### Explanation:

I'm going to assume you mean population variance (sample variance will differ slightly).

${\sigma}^{2} = \frac{\Sigma {x}^{2} - {\left(\Sigma x\right)}^{2} / N}{N}$

Please differentiate between the two. The first sign says "add the squares of your numbers", the second says "add first, THEN square the sum"

$\Sigma {x}^{2} = {15}^{2} + {4}^{2} + \ldots + {10}^{2} = 458$
${\left(\Sigma x\right)}^{2} = {\left(15 + 4 + 2 + \ldots\right)}^{2} = 1024$
$N = 6$

${\sigma}^{2} = \frac{458 - \left(\frac{1024}{6}\right)}{6} = 47.9$