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Mean Absolute Deviation (MAD)
Mean absolute deviation, or “MAD”, is the average distance of all data points from the mean.
It is a way of looking at variability (spread) in a data set.
To calculate the mean, follow these 3 easy steps:
1 – Calculate the mean of the data.
2 – Determine the distance of each piece of data from the mean.
3 – Find the mean of these distances.
Example 1: Pets R Us recorded the number of fish purchased by customers on Saturday. They had
twelve customers that bought fish, and the numbers of fish purchased are: 10, 2, 1, 1, 1, 10, 8, 1, 5,
10, 10, and 1. Determine the mean absolute deviation.
Step 1: Find the mean:
10  2  1  1  1  10  8  1  5  10  10  1 60

5
12
12
Step 2: Determine the distance of each piece of data from the mean.
** HINT: Two helpful strategies for this are to use a TABLE or a DOT PLOT!! **
All data points are on the dot plot:
Then, write the distances of each data from the mean:
4  4  4  4  4  3  0  3  5  5 + 5 + 5 46

 3.83
12
12
The MAD is 3.83. This means that the average distance from the mean is 3.83.
Step 3: Find the mean of the distances:
Example 2: Find the MAD of guests’ ages at twins Solomon’s and Sofia’s party: 4, 6, 5, 6, 6, and 9.
Step 1: Find the mean:
4  6  5  6  6  9 36

6
6
6
Step 2: Determine the distance of each piece of data from the mean.
Age Distance from mean of 6
4
2
6
0
5
1
6
0
6
0
9
3
Step 3: Find the mean of the distances:
2  0  1  0  0  3 6
 1
6
6
The MAD is 1. This means the average distance from the mean is 1.
Let’s show “MAD” who’s boss!!
Find the MAD for each set of data below!
1) Number of pets owned by students in Spanish Club: 5, 6, 3, 3, 4, and 3 .
Step 1: Find the mean.
Step 2: Determine the distance of each piece of data from the mean.
(Hint: use a table or dot plot!)
Step 3: Find the mean of the distances.
The MAD is___________.
2) Number of pets owned by students in the Young Vets Club: 8, 2, 3, 1, 8, 1, 0, and 9.
3) Notice that both problems above had the same mean of __________. But, the MADs were different. The
MAD for problem #2 was _______________ than the MAD for problem #1. What does this tell you about
the data?