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.

Here is the correct work. The picture is not showing up, but you can compare this work to what is given.

To find the mean, you will find the sum of all the numbers and divide by how many numbers there are.

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

To find the mean absolute deviation, you find how far away each of the numbers are from the mean.  Find the sum of these and divide by the same number of numbers.

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

The MAD is 10.

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