Mean absolute deviation

The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.
Here's how to calculate the mean absolute deviation.
Step 1: Calculate the mean.
Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.
Step 3: Add those deviations together.
Step 4: Divide the sum by the number of data points.
Following these steps in the example below is probably the best way to learn about mean absolute deviation, but here is a more formal way to write the steps in a formula:
MAD=xix¯n\text{MAD}=\dfrac{\sum{\lvert x_i-\bar{x} \rvert}}{n}

Example

Erica enjoys posting pictures of her cat online. Here's how many "likes" the past 6 pictures each received:
10, 15, 15, 17, 18, 21
Find the mean absolute deviation.
Step 1: Calculate the mean.
The sum of the data is 96 total "likes" and there are 6 pictures.
m, e, a, n, equals, start fraction, 96, divided by, 6, end fraction, equals, 16
The mean is 16.
Step 2: Calculate the distance between each data point and the mean.
Data pointDistance from mean
10open vertical bar, 10, minus, 16, close vertical bar, equals, 6
15open vertical bar, 15, minus, 16, close vertical bar, equals, 1
15open vertical bar, 15, minus, 16, close vertical bar, equals, 1
17open vertical bar, 17, minus, 16, close vertical bar, equals, 1
18open vertical bar, 18, minus, 16, close vertical bar, equals, 2
21open vertical bar, 21, minus, 16, close vertical bar, equals, 5
Step 3: Add the distances together.
6, plus, 1, plus, 1, plus, 1, plus, 2, plus, 5, equals, 16
Step 4: Divide the sum by the number of data points.
M, A, D, equals, start fraction, 16, divided by, 6, end fraction, approximately equals, 2, point, 67 likes
On average, each picture was about 3 likes away from the mean.
Want to learn more about mean absolute deviation? Check out this video.

Practice problem

The following table shows the number of lemons that grew on Mary's lemon tree each season.
SeasonNumber of lemons
Winter3
Spring15
Summer21
Fall13
Find the mean absolute deviation (MAD) of the data set.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i
lemons

Want to practice more problems like these? Check out this exercise.