What Is MAD in Math?
In math classes, MAD means mean absolute deviation: the average distance of the values in a data set from the mean. A small MAD says the values cluster near the mean, and a large MAD says they are spread out.
Enter your data and follow the steps: find the mean, find each value's distance from it ignoring the sign, add the distances, and divide by the number of values. Add a second data set to compare how variable the two are and how far apart their means sit in MADs.
This is the version of MAD used in middle school and introductory statistics. It differs from the median absolute deviation, which uses the median and is more resistant to outliers.
How to Use the MAD in Math Calculator
- Enter your data set.
- Optionally enter a second set to compare.
- Follow the five steps: mean, distances, add, divide, compare.
MAD in Math Formula
Mean absolute deviation
Mean
MAD in Math Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| x | Each data value | |
| x̄ | Mean of the data | |
| |x − x̄| | Distance of a value from the mean | Always zero or positive |
| n | Number of values | |
| MAD | Mean absolute deviation | Σ|x − x̄| / n |
MAD in Math Worked Example
With the example values loaded in the calculator above, the steps are:
- Add the values and divide by 6 to find the mean: 5.5.
- Find how far each value is from the mean. Ignore the sign, so every distance is positive.
- Add the distances: 9.
- Divide by 6: MAD = 1.5.
- Repeat for the second set to get MAD = 0.666667, then compare the two.
Result: Mean absolute deviation (MAD) = 1.5; Second set: MAD = 0.666667.
Worked example: 4, 8, 6, 5, 3, 7
The mean is 33 ÷ 6 = 5.5. The distances from the mean are 1.5, 2.5, 0.5, 0.5, 2.5 and 1.5, which add to 9.
MAD = 9 ÷ 6 = 1.5. On average, the values are 1.5 away from the mean.
Comparing two data sets
A second set 5, 6, 5, 7, 6, 5 has mean 5.6667 and MAD 0.6667. Its values stay closer to its mean, so it is less variable than the first set, even though the two means are close.
Where MAD in Math Is Used
Homework and tests
Check each step of a MAD problem.
Comparing two groups
Say which of two data sets is more variable, such as two classes' scores.
Quick spread measure
Describe spread in plain words without squaring deviations.
Common MAD in Math Mistakes to Avoid
- Always take the distance without the sign. Without it, the deviations would add to 0.
- A MAD of 0 means every value equals the mean.
MAD in Math Terms and Definitions
- MAD
- Mean absolute deviation: the average of the absolute distances from the mean.
MAD in Math FAQs
What does MAD mean in math?
Mean absolute deviation, the average distance of the data from the mean.
How do you find the MAD?
Find the mean, find each value’s distance from it, add the distances and divide by the number of values.
Why use absolute values?
Deviations above and below the mean would cancel to 0. Absolute values count all distances as positive.
What does a larger MAD mean?
The data are more spread out around the mean.
Is MAD the same as standard deviation?
No. Standard deviation squares the deviations, so it gives extra weight to values far from the mean. MAD is usually smaller.
Can I compare two data sets with MAD?
Yes. Enter a second set. The one with the larger MAD is more variable.