Question

A store manager is looking at past jewelry sales to determine what sizes of rings to keep in stock. The list shows the ring sizes purchased by the last ten jewelry customers.

9, 7, 6.5, 7.5, 7, 8, 5, 6, 7.5, 8
What is the variance of the data? Round to the nearest hundredths.

Answer 1

Variance is the average of the square of the differences of each data with the mean. To calculate for the variance, we first calculate for the mean. Then, we subtract each data with the mean. Next, each difference would be squared and added. The resulting value would be divided on how many data are used. We calculate as follows:

Mean = 9 + 7 + 6.5 + 7.5 + 7 + 8 + 5 + 6 + 7.5 + 8 / 10
Mean = 6.4

Squared of the sum of the differences = (9-6.4)^2 + (7-6.4)^2 + (6.5-6.4)^2 + (7.5-6.4)^2 + (7-6.4)^2 + (8-6.4)^2 + (5-6.4)^2 + (6-6.4)^2 + (7.5-6.4)^2 + (8-6.4)^2 = 17.15

Variance = 17.15 / 10 = 1.715