Question

Stefano calculated the mean absolute deviation for the data set 32, 4, 12, 40, 20, and 24. His work is shown below. Step 1: Find the mean. mc006-1.jpg Step 2: Find each absolute deviation. 10, 18, 10, 18, 2, 2 Step 3: Find the mean absolute deviation. mc006-2.jpg What is Stefano’s error? Stefano should have divided by 5 when finding the mean. Stefano found the absolute deviation of 20 incorrectly. Stefano should have divided by 6 when finding the mean absolute deviation. Stefano did not find the correct value for the mean.

Answer 1

To find the mean, you add all the numbers together and then divide by the number of numbers (6).

4 + 12 + 20 + 24 + 32 + 40 =  132
132/6 = 22

To find the mean absolute deviation, you will find the distance between each number and the mean and then divide this by 6 as well.

(22-4) +(22-12)+(22-20)+(24-22)+(32-22)+(40-22)
18 + 10 + 2 + 2 + 10 + 18 = 60
60/6 = 10

The mean absolute deviation is 10.

The correct answer is that Stefano should have divided by 6 when finding the mean absolute deviation.