What Is Mean Average Deviation?
The mean average deviation measures spread as the average absolute distance of the values from their mean. A larger value means the data are more spread out.
Enter one data set for its mean and deviation with a full working table, or add a second set to compare. The comparison gives the difference of the means in units of the average deviation, which shows how much the two sets overlap.
The sections below give the formula, a worked example comparing two sets and answers about how this differs from standard deviation.
How to Use the Mean Average Deviation Calculator
- Enter data set A.
- Optionally enter data set B to compare.
- Read each mean and mean average deviation.
- Use the difference in MAD units to judge how much the sets overlap.
Mean Average Deviation Formula
Mean average deviation
Gap in MAD units
Mean Average Deviation Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| x̄ | Mean of the data set | |
| |x − x̄| | Absolute deviation of a value | |
| n | Number of values | |
| MAD | Mean average deviation |
Mean Average Deviation Worked Example
For 4, 6, 8, 10 the mean is 7. The absolute deviations are 3, 1, 1, 3, whose sum is 8, so the mean average deviation is 8 ÷ 4 = 2. A second set with mean 13 and deviation 2 has means 6 apart, which is 3 times the average deviation.
With the example values loaded in the calculator above, the steps are:
- Mean of A = 14.142857.
- Absolute deviations |x − 14.1429| for each value are added: 13.142857.
- Mean average deviation = 13.142857 ÷ 7 = 1.877551.
- Mean of B = 24.285714; its mean average deviation = 2.8979592.
- The means differ by 10.1429, which is 4.248 times the average of the two deviations.
Result: Mean of A = 14.142857; Mean average deviation of A = 1.877551; Mean of B = 24.285714; Mean average deviation of B = 2.8979592.
How to Read the Mean Average Deviation
The mean average deviation is the average distance of the values from their mean, ignoring sign. For 4, 6, 8, 10 the mean is 7, the distances are 3, 1, 1 and 3, and their average is 2. Values in this set sit about 2 units from the centre.
When you compare two sets, look at both the gap between the means and the typical spread. A second set with mean 13 and deviation 2 has a mean 6 units higher, which is three times the deviation. That gap is large compared with the spread, so the sets barely overlap.
Where Mean Average Deviation Is Used
Describing spread
Report how far values typically sit from the mean, in the units of the data.
Comparing two sets
Put two data sets side by side and see which is more variable and how far apart the means are.
Teaching
The working table shows each deviation, so students see where the average comes from.
Seventh-grade statistics
Match the "mean absolute deviation" work found in many middle-school courses.
Common Mean Average Deviation Mistakes to Avoid
- Take absolute values before averaging. Plain deviations from the mean always sum to zero.
- This measure uses the mean as the centre. A version around the median gives a different number.
- Mean average deviation is smaller than the standard deviation for most data, so do not compare the two directly.
- Compare the difference between means with the deviation to judge how much the sets overlap.
Mean Average Deviation Terms and Definitions
- Mean average deviation
- The average absolute distance of values from their mean.
Mean Average Deviation FAQs
How do you calculate the mean average deviation?
Find the mean, take the absolute difference of each value from it, and average those differences. For 4, 6, 8, 10 the absolute differences are 3, 1, 1, 3 and the average is 2.
How do I compare two data sets with MAD?
Compare the means, then compare how large each MAD is. If the gap between the means is several times the MAD, the sets are clearly separated. If it is smaller than the MAD, they overlap heavily.
What does a larger mean average deviation mean?
It means the values are more spread out around the mean. A set with a MAD of 5 is more variable than one with a MAD of 2, if the two are measured in the same units.
Is it the same as standard deviation?
No. The standard deviation squares the deviations before averaging and then takes the square root, so it weights large deviations more. For the same data it is usually larger.