Using it's concept, it is found that the variance of the data-set is of 1.15.
The mean of a data-set is the sum of all observations divided by the number of observations, hence:
[tex]E(X) = \frac{9 + 7 + 6.5 + 7.5 + 7 + 8 + 5 + 6 + 7.5 + 8}{10} = 7.15[/tex]
The variance is the sum of the differences square between each value and the mean, divided by the number of values. Hence:
[tex]V(X) = \frac{1}{10}[(9 - 7.15)^2 + (7 - 7.15)^2 + (6.5 - 7.15)^2 + (7.5 - 7.15)^2 + (7 - 7.15)^2 + (8 - 7.15)^2 + (5 - 7.15)^2 + (6 - 7.15)^2 + (7.5 - 7.15)^2 + (8 - 7.15)^2] = 1.15[/tex]
A similar problem is given at https://brainly.com/question/1527299
