Introduction
The Mean Absolute Deviation (MAD) tells you how spread out a set of numbers is. It is the average distance between each value and the mean. A small MAD means your numbers sit close together. A large MAD means they are spread far apart.
This MAD calculator runs each step of the calculation. Type or paste your numbers, separated by commas, spaces, or new lines. Press Calculate. You get the mean absolute deviation, the mean, the sample size, and the sum of the absolute deviations.
You also get more than just an answer. The tool shows a chart of how far each point sits from the mean, a full table of deviations, and a step-by-step solution so you can check the math or study it. You can pick how many decimal places you want, download your results as a CSV file, and copy R code to run the same calculation yourself.
Use it for homework, class notes, lab data, or any time you need a quick and clear measure of spread.
How to use our Mean Absolute Deviation (MAD) Calculator
Type your numbers into the calculator and pick how many decimal places you want. The tool gives you the mean absolute deviation, the mean, the sample size, the sum of the absolute deviations, a chart, and step-by-step math.
Data Set (X): Enter your numbers in the big box. You can split them with commas, spaces, or new lines. Words and blank spots are skipped. The live preview shows how many valid numbers the calculator found.
Example data sets: Click one of the three example buttons to load a ready-made set of numbers. This is a fast way to see how the MAD formula works.
On-screen number pad: Tap the keys to add digits, a comma, a space, or a decimal point. Use the arrow key to delete one character or CLEAR to empty the box.
Decimal Precision: Choose 1 to 9 decimal places. This rounds the MAD, the mean, and every other number in the results and table.
Calculate: Press this button to get your answer. Press Reset to clear the box and start over.
What Is Mean Absolute Deviation (MAD)?
Mean absolute deviation, or MAD, tells you how spread out a set of numbers is. It is the average distance between each number and the mean (the average) of the data set. A small MAD means the numbers sit close together. A large MAD means they are spread far apart. Other common measures of spread include the range, the interquartile range, and the variance.
The MAD Formula
The formula is:
MAD = Σ |xᵢ − x̄| ÷ n
- xᵢ: each value in your data set
- x̄: the mean of all the values
- n: how many values you have
- | |: absolute value, which turns negative numbers into positive ones
How to Find MAD in 4 Steps
- Find the mean. Add all the values, then divide by how many there are.
- Find each deviation. Subtract the mean from every value.
- Drop the minus signs. Take the absolute value of each deviation, then add them all up.
- Divide by n. That answer is the MAD.
A Quick Example
Take the data set 4, 7, 13, 2, 1, 8. The sum is 35, so the mean is 35 ÷ 6 = 5.8333. The distances from the mean are 1.8333, 1.1667, 7.1667, 3.8333, 4.8333, and 2.1667. Those add up to 21. Divide by 6 and the MAD is 3.5. On average, each value sits about 3.5 units away from the mean.
Why MAD Matters
MAD is one of the easiest ways to measure spread. Unlike standard deviation, it does not square anything, so the answer stays in the same units as your data. That makes it simple to explain. It is also less affected by one very large or very small value, since it does not blow up big gaps the way squaring does.
Things to Remember
- MAD is never negative. The smallest it can be is 0.
- MAD equals 0 only when every value in the set is the same.
- The deviations always add up to 0 before you take absolute values. That is why the absolute value step is needed.
- MAD uses the same units as your data. If you measure in dollars, the MAD is in dollars.
- Do not confuse mean absolute deviation with median absolute deviation. Both are called "MAD," but the second one uses the median instead of the mean.
- MAD is not the same as a z score, which measures one value's distance from the mean in standard deviations.
Where MAD Is Used
Teachers use MAD in middle school math to introduce spread. Businesses use it to check how far sales forecasts miss real sales. Scientists use it to see how much repeated measurements vary. Anytime you want a plain answer to "how different are these numbers?", MAD works well.