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 given by s^2 = [summation (x - mean) ^2] / n.

mean = (90 + 75 + 72 + 88 + 85) / 5 = 82

Variance = [ (90 - 82) ^2 + (75 - 82) ^2 + (72 - 82) ^2 + (88 - 82) ^2 + (85 - 82) ] / 5

= [8^2 + (-7) ^2 + (-10) ^2 + 6^2 + 3^2] / 5

= (64 + 49 + 100 + 36 + 9] / 5

= 258 / 5

Therefore, the value of the numerator of the calculation of the variance of the data set is 258.