Mean Absolute Deviation Calculator

What is a mean absolute deviation calculator?

A mean absolute deviation calculator measures how spread out a set of numbers is by averaging how far each value lies from the mean. Enter your data points and the calculator instantly reports the mean absolute deviation (MAD) along with the mean and the count of values. A small MAD means the numbers cluster tightly around the average; a large MAD means they are widely scattered.

Unlike the standard deviation, which squares each deviation, the mean absolute deviation uses the plain absolute distance. This keeps the result in the same units as the original data and makes it intuitive: the MAD is simply the typical distance between a data point and the mean.

How does it work?

The mean absolute deviation is the average of the absolute differences between each value and the mean:

where $\bar{x}$ is the mean of the data and $n$ is the number of values. The calculation follows three steps:

1. Find the mean by adding all the values and dividing by how many there are.
2. Find each absolute deviation by subtracting the mean from every value and dropping the sign with the absolute value.
3. Average those absolute deviations by adding them up and dividing by $n$.

Taking the absolute value in step 2 is what distinguishes the MAD from a naive average deviation: without it, the positive and negative deviations would always cancel out to zero.

Worked examples

Consider the data set $1, 2, 3, 4, 5$, which has $n = 5$ values.

First, the mean:

Next, the absolute deviations from the mean of $3$ are $2, 1, 0, 1, 2$, which sum to $6$. The mean absolute deviation is:

For the set $2, 2, 4, 4$ the mean is $3$, the absolute deviations are $1, 1, 1, 1$, and so:

When every value is identical, such as $10, 10, 10$, the mean is $10$, every deviation is $0$, and the mean absolute deviation is $0$ — there is no spread at all.

Practical notes

The mean absolute deviation is popular when you want a measure of variability that is easy to explain and resistant to the outsized influence of extreme values. Because it does not square the deviations, a single far-away point pulls the MAD up less than it pulls up the standard deviation, making the MAD a more robust summary of typical spread.

It pairs naturally with the average, which provides the central value the deviations are measured from, and with the mean, median and mode for a fuller picture of a data set’s center and shape. The MAD can never be negative, and it is zero only when every value equals the mean.