Question

Find the variance of [6 ,7 ,10 ,11 ,12 ,13 ,16 ,18 ,25].

Answer 1

The variance of [6 ,7 ,10 ,11 ,12 ,13 ,16 ,18 ,25] is 34.61

The sample size (n) = 9

The mean of the distribution (x_i) is the sum of the distribution divided by the number of items in the distribution.

$\mathbf{x_i=\dfrac{6+7+10+11+12+13+16+18+25}{9}}$

$\mathbf{x_i=\dfrac{118}{9}}$

$\mathbf{x_i=13.11}$

The variance  is the average between the difference of the mean, followed by squaring the result.

$\mathbf{S^2 = \dfrac{\sum (x_i - \bar x)^2}{n-1}}$

$\mathbf{S^2 = \dfrac{ ((6 -13.11)^2+ (7-13.11)^2+...+(16-13.11)^2+(18-13.11)^2+(25-13.11)^2}{8}}$

$\mathbf{S^2 = \dfrac{276.8889}{8}}$

$\mathbf{S^2 = \ 34.61}$

Therefore, the variance of the sample given is 34.61

Learn more about variance here:

brainly.com/question/13091634?referrer=searchResults