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.
[tex]\mathbf{x_i=\dfrac{6+7+10+11+12+13+16+18+25}{9}}[/tex]
[tex]\mathbf{x_i=\dfrac{118}{9}}[/tex]
[tex]\mathbf{x_i=13.11}[/tex]
The variance is the average between the difference of the mean, followed by squaring the result.
[tex]\mathbf{S^2 = \dfrac{\sum (x_i - \bar x)^2}{n-1}}[/tex]
[tex]\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}}[/tex]
[tex]\mathbf{S^2 = \dfrac{276.8889}{8}}[/tex]
[tex]\mathbf{S^2 = \ 34.61}[/tex]
Therefore, the variance of the sample given is 34.61
Learn more about variance here:
https://brainly.com/question/13091634?referrer=searchResults
