# What is the variance of {-3, -6, 7, 0, 3, -2}?

Jun 17, 2018

$\frac{211}{2} \mathmr{and} 105.5$

#### Explanation:

find the mean:

$- 3 + - 6 + 7 + 0 + 3 + 2 = 3$

$\frac{3}{6} = \frac{1}{2}$

subtract the mean from each number in the data and square the result:

$- 3 - \frac{1}{2} = - \frac{7}{2}$
$- 6 - \frac{1}{2} = - \frac{13}{2}$
$7 - \frac{1}{2} = \frac{13}{2}$
$0 - \frac{1}{2} = - \frac{1}{2}$
$3 - \frac{1}{2} = \frac{5}{2}$
$2 - \frac{1}{2} = \frac{3}{2}$

${\left(- \frac{7}{2}\right)}^{2} = \frac{49}{4}$
${\left(- \frac{13}{2}\right)}^{2} = \frac{169}{4}$
${\left(\frac{13}{2}\right)}^{2} = \frac{169}{4}$
${\left(- \frac{1}{2}\right)}^{2} = \frac{1}{4}$
${\left(\frac{5}{2}\right)}^{2} = \frac{25}{4}$
${\left(\frac{3}{2}\right)}^{2} = \frac{9}{4}$

find the mean of the squared differences:

$\frac{49}{4} + \frac{169}{4} + \frac{169}{4} + \frac{1}{4} + \frac{25}{4} + \frac{9}{4} = \frac{422}{4} = \frac{211}{2} \mathmr{and} 105.5$