# What is the variance of the following numbers?: 63, 54, 62, 59, 52,

Dec 27, 2015

${\sigma}^{2} = 18.8$

#### Explanation:

$m e a n = \frac{63 + 54 + 62 + 59 + 52}{5}$
$m e a n = 58$
$n = 5$

63
$x - m e a n = 63 - 58 = 5$
${\left(x - m e a n\right)}^{2} = {5}^{2} = 25$

54
$x - m e a n = 54 - 58 = - 4$
${\left(x - m e a n\right)}^{2} = {\left(- 4\right)}^{2} = 16$

62
$x - m e a n = 62 - 58 = 4$
${\left(x - m e a n\right)}^{2} = {4}^{2} = 16$

59
$x - m e a n = 59 - 58 = 1$
${\left(x - m e a n\right)}^{2} = {1}^{2} = 1$

52
$x - m e a n = 52 - 58 = - 6$
${\left(x - m e a n\right)}^{2} = {\left(- 6\right)}^{2} = 36$

$\Sigma {\left(x - m e a n\right)}^{2} = 25 + 16 + 16 + 1 + 36 = 94$

${\sigma}^{2} = \frac{\Sigma {\left(x - m e a n\right)}^{2}}{n} = \frac{94}{5} = 18.8$