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## Statistics and probability

### Course: Statistics and probability>Unit 3

Lesson 8: Other measures of spread

# Mean absolute deviation (MAD) review

## 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:
$\text{MAD}=\frac{\sum |{x}_{i}-\overline{x}|}{n}$

### 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.
$\text{mean}=\frac{96}{6}=16$
The mean is $16$.
Step 2: Calculate the distance between each data point and the mean.
Data pointDistance from mean
$10$$|10-16|=6$
$15$$|15-16|=1$
$15$$|15-16|=1$
$17$$|17-16|=1$
$18$$|18-16|=2$
$21$$|21-16|=5$
Step 3: Add the distances together.
$6+1+1+1+2+5=16$
Step 4: Divide the sum by the number of data points.
$\text{MAD}=\frac{16}{6}\approx 2.67$ likes
On average, each picture was about $3$ likes away from the mean.

### Practice problem

The following table shows the number of lemons that grew on Mary's lemon tree each season.
SeasonNumber of lemons
Winter$3$
Spring$15$
Summer$21$
Fall$13$
Find the mean absolute deviation (MAD) of the data set.
lemons

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