Question

A comparison of coffee prices at 4 randomly selected grocery stores in San Diego showed increases from the previous month of 12, 15, 17, and 20 cents for a 200-gram jar. Find the variance of this random sample of prices increase.

A. 9
B. 16
C. 25
D. 36

Answer 1

The variance of the random sample of price increases is 8.5.

Step-by-step explanation:

To find the variance of the random sample of price increases, we first need to calculate the mean increase. The mean increase is the sum of all the increases divided by the number of increases.

Mean increase = (12 + 15 + 17 + 20) / 4 = 16

Next, we calculate the deviation from the mean for each increase by subtracting the mean increase from each individual increase.

Deviation from mean = (12 - 16, 15 - 16, 17 - 16, 20 - 16) = (-4, -1, 1, 4)

Then, we square each deviation from the mean.

(-4)^2 = 16, (-1)^2 = 1, (1)^2 = 1, (4)^2 = 16

Finally, we calculate the variance by finding the average of the squared deviations.

Variance = (16 + 1 + 1 + 16) / 4 = 34 / 4 = 8.5