Math
Mean Absolute Deviation Calculator
Compute mean absolute deviation (MAD) from the mean and from the median for any list of numbers. Returns count, sum, mean, median, min, max, range, and a per-value deviation breakdown.
Enter your numbers
Decimals and negatives work. Non-numeric tokens are ignored.
MAD from mean
1.5
MAD from median
1.5
Count
8
Sum
40
Mean
5
Median
4.5
Min
2
Max
9
Range
7
Step by step (mean = 5, median = 4.5)
| Value (x) | |x - mean| | |x - median| |
|---|---|---|
| 2 | 3 | 2.5 |
| 4 | 1 | 0.5 |
| 4 | 1 | 0.5 |
| 4 | 1 | 0.5 |
| 5 | 0 | 0.5 |
| 5 | 0 | 0.5 |
| 7 | 2 | 2.5 |
| 9 | 4 | 4.5 |
Frequently Asked Questions about the Mean Absolute Deviation Calculator
What is mean absolute deviation (MAD)?
Mean absolute deviation is the average distance every value sits from the center of the dataset. You pick a center (mean or median), measure how far each value falls from it, drop the sign so positive and negative gaps both count as distance, and average those distances. A small MAD means the data is tightly packed around the center; a large MAD means it is spread out.
What is the difference between MAD from the mean and MAD from the median?
MAD from the mean uses the arithmetic mean as the center: Σ|xi - mean| / n. MAD from the median uses the median: Σ|xi - median| / n. The median version is more robust because a single extreme value can shift the mean far away from the bulk of the data, which inflates MAD from the mean. The median barely moves, so MAD from the median stays closer to the typical gap and is the better choice for skewed datasets or data with outliers.
Why teach MAD before standard deviation?
MAD uses one idea kids already understand: distance. You subtract, take the absolute value, and average. Standard deviation squares each gap, averages the squares, then takes a square root, so the units are easier to lose track of and the intuition is buried. MAD lands in the same units as the data, so a MAD of 3 minutes on commute times literally means the average commute differs from the typical commute by about 3 minutes. That is why the Common Core introduces MAD in 6th grade and saves variance and standard deviation for later.
When does MAD beat variance and standard deviation?
MAD wins on three fronts. First, robustness: MAD (especially MAD from the median) is far less sensitive to outliers than variance, because squaring amplifies extreme gaps. Second, interpretability: MAD reports a real, in-units distance, while variance is in squared units. Third, teaching: MAD needs only subtraction, absolute value, and division. Variance still wins when you need the math to plug into normal-theory tests, regression, or formulas where squared deviations are required by the algebra (Pythagorean decompositions of variance, least squares, ANOVA).
Can you walk through the [2, 4, 4, 4, 5, 5, 7, 9] example?
Sum is 40 and count is 8, so the mean is 5 and the median is 4.5 (average of the two middle values 4 and 5). For MAD from the mean, take |xi - 5| for each value: 3, 1, 1, 1, 0, 0, 2, 4. They sum to 12, and 12 / 8 = 1.5. For MAD from the median, take |xi - 4.5|: 2.5, 0.5, 0.5, 0.5, 0.5, 0.5, 2.5, 4.5. They sum to 12 as well, so MAD from the median is also 1.5. In symmetric or near-symmetric data, the two MADs often match; on skewed data they pull apart.