The test scores of a geometry class are given below.
90, 75, 72, 88, 85
the teacher wants to find the variance for the class population. what is the value of the numerator of the calculation of the variance?

Variance is the difference of the number from the mean of the group of numbers then square it and find the average. In this case, we need to find the mean first. 90 + 75 + 72 + 88 + 85 = 410/5 = 82 . Now we must get the difference of each from the mean. 
90 - 82 = 8
75 - 82 = -7
72 - 82 = -10
88 - 82 = 6
85 - 82 = 3
Next is to find the average of the square of the numbers.
(8^2) + (-7^2) + (-10^2) + (6^2) + (3^2) is
64 + 49 + 100 + 36 + 6 = 255. Next step is to simply divide it by 5. The numerator in calculating the variance is the sum of the square of the numbers which is 255.