Mean Absolute Deviation Calculator

Mean absolute deviation (MAD) is the average distance between each value and the mean. Enter your numbers to get the MAD with every |x − x̄| listed, plus the standard deviation for comparison.

6 values read.

Mean absolute deviation
3
Mean
7
Sum of |x − x̄|
18
Sample SD (compare)
3.7417
Count
6
±1 SD24681012
▲ mean 7 · ◆ median 7 · shaded band = mean ± 1 SD (3.2583 to 10.7417)

Step-by-step working

  1. Add the values and divide by the count to get the meanx̄ = (2 + 4 + 6 + 8 + 10 + 12) ÷ 6 = 42 ÷ 6 = 7
  2. Find each absolute deviation |x − x̄||2 − 7| = 5 |4 − 7| = 3 |6 − 7| = 1 |8 − 7| = 1 |10 − 7| = 3 |12 − 7| = 5
  3. Average the absolute deviationsMAD = 18 ÷ 6 = 3

Formula MAD = Σ|x − x̄| ÷ n

Ask the tutor about your result

An AI tutor reads your inputs and results above and explains them in plain English. The numbers come from the calculator; the explanation is AI-written, so check it against your notes.

How to calculate mean absolute deviation

  1. Find the mean x̄.
  2. Subtract the mean from each value and drop the sign (take the absolute value).
  3. Add those distances and divide by the number of values.

Example: 2, 4, 6, 8, 10, 12 has mean 7. The distances are 5, 3, 1, 1, 3, 5, which add to 18, so MAD = 18 ÷ 6 = 3.

MAD vs standard deviation

Both measure spread around the mean. MAD uses absolute values, so it is easier to explain (“values are 3 away from the mean on average”). Standard deviation squares the distances first, which gives large deviations more weight; it is always at least as large as the MAD and is the measure used in most further statistics. Middle-school courses (including the US Common Core, grade 6) teach MAD first for exactly this reason.

Frequently asked questions

Is mean absolute deviation the same as median absolute deviation?

No. Mean absolute deviation averages distances from the mean. Median absolute deviation takes the median of distances from the median, and is used in robust statistics. Both are sometimes abbreviated MAD; this calculator gives the mean version taught in school.

Can MAD be zero?

Only if every value is identical, so every distance from the mean is zero.

Does MAD use n or n − 1?

n. There is no sample correction in the usual definition.