Mean Absolute Deviation Calculator

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The mean absolute deviation (MAD) is the average distance between each value and the mean. For 2, 4, 6, 8, 10 the mean is 6, the distances are 4, 2, 0, 2, 4 and the MAD is 12 ÷ 5 = 2.4.

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Data (separate with commas or spaces)

Distance from

Mean absolute deviation

2.4

On average the values are 2.4 away from the mean (6).

Value → distance from the mean
2	\|2 − 6\| = 4
4	\|4 − 6\| = 2
6	\|6 − 6\| = 0
8	\|8 − 6\| = 2
10	\|10 − 6\| = 4
Summary
Count	5
Mean	6
Median	6
Sum of distances	12
Mean absolute deviation	2.4
Median absolute deviation	2
Population standard deviation	2.828427

Show steps

Mean = 6 (sum 30 ÷ 5).
Find each distance |x − 6| and add them: 12.
MAD = 12 ÷ 5 = 2.4.

How to use the calculator

Type or paste your numbers, separated by commas, spaces or new lines.
Keep “the mean” for the usual mean absolute deviation, or switch to the median.
Press Calculate to see each distance, the MAD and related measures.

MAD formula and steps

MAD = Σ|x − x̄| ÷ n

Find the mean x̄.
Subtract the mean from each value and drop the sign (take the absolute value).
Add the distances.
Divide by how many values there are.

Value	Distance from mean 6
2	4
4	2
6	0
8	2
10	4
Sum	12

MAD = 12 ÷ 5 = 2.4.

MAD vs standard deviation

Both measure spread. The MAD averages plain distances, so it is easy to explain: “a typical value is 2.4 away from the mean”. The standard deviation squares the distances before averaging, which gives more weight to values far from the mean. For 2, 4, 6, 8, 10 the population standard deviation is 2.83, a little larger than the MAD of 2.4.

The median absolute deviation is a different measure: the median of the distances from the median. It is very resistant to outliers.

Mean absolute deviation practice questions

Test yourself with 6 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

How do you find the mean absolute deviation?

Find the mean, find how far each value is from it (ignoring signs), add the distances and divide by the number of values.

What does the MAD tell you?

It is the average distance from the mean, so it tells you how much a typical value differs from the center. A small MAD means the data are bunched together.

Is MAD the same as standard deviation?

No. Both measure spread, but the standard deviation squares the distances first, so it is affected more by values far from the mean. It is usually a little larger than the MAD.

What is the median absolute deviation?

It is the median of the absolute distances from the median. It ignores extreme values almost completely, so it is used when data have outliers.

Sources

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Effortless Math Team

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Effortless Math Team

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