Mean Absolute Deviation Calculator
Find the mean absolute deviation (MAD) of your data around the mean or the median. See every absolute deviation and a clear step-by-step solution.
Mean Absolute Deviation Calculator
Enter your numbers below and get your result instantly.
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Step-by-Step Solution
What Is the Mean Absolute Deviation?
The mean absolute deviation (MAD) tells you, on average, how far the values in a data set are from the center of the data. A small MAD means the values are close together. A large MAD means they are spread out.
It is called “absolute” because every distance is taken as a positive number, so values below the center do not cancel out values above it.
The center is usually the mean, but some textbooks use the median instead. Our calculator lets you choose either one.
How to Calculate the Mean Absolute Deviation
You can find the MAD by hand in four steps.
1. Find the mean
Add all the values and divide by how many there are. You can check this with our Average Calculator.
2. Find the distance of each value from the mean
Subtract the mean from each value, and ignore any minus sign. This gives the absolute deviation of each value.
3. Add the absolute deviations
Add up all the distances from step 2.
4. Divide by the number of values
Divide the total by n. The result is the mean absolute deviation.
Mean Absolute Deviation Examples
Example 1: five values
The mean is 30. The distances from the mean are 20, 10, 0, 10 and 20, which add up to 60. Dividing by 5 gives a MAD of 12.
Example 2: eight values
The mean is 5. The distances are 3, 1, 1, 1, 0, 0, 2 and 4, which add up to 12. Dividing by 8 gives a MAD of 1.5.
Example 3: around the median
The mean is about 5.2857, and the MAD around the mean is about 2.5306. The median is 6, so the distances from the median are 5, 3, 3, 0, 1, 2 and 3, which add up to 17. Dividing by 7 gives a MAD around the median of about 2.4286.
Mean Absolute Deviation vs Median Absolute Deviation
These two names sound alike, but they are different measures.
- Mean absolute deviation: the average of the absolute distances from the center. This is the main result of our calculator.
- Median absolute deviation: the median of the absolute distances from the median. It is even less affected by extreme values. Our calculator shows it as an extra result.
When a textbook or a teacher says “MAD”, check which one they mean.
MAD vs Standard Deviation
Both measure how spread out data is. The standard deviation squares the distances before averaging, so large distances count for more. The MAD treats every distance equally, which makes it easier to understand and to calculate by hand.
For the data 10, 20, 30, 40, 50, the MAD is 12 and the population standard deviation is about 14.14. The standard deviation is usually a little larger than the MAD. If you need the standard deviation, use our Standard Deviation Calculator, and for the simplest spread measure see the Range Calculator.
Should I Use the Mean or the Median as the Center?
Use the mean in most cases, because that is the standard definition. Use the median if your data has extreme values and you want a measure that is not pulled so much by them. You can find the median with our Median Calculator.
More Mean Absolute Deviation Examples
These extra worked examples compare the MAD with the standard deviation, show what one extreme value does to it, compare two data sets with the same mean, and use decimal values. Remember that MAD is the sum of the absolute distances from the center, divided by n.
Example 4: MAD and standard deviation side by side
Find the MAD and the population standard deviation of 3, 5, 8, 12, 17.
Answer: the MAD is 4.4, and the population standard deviation is about 5.0200.
The mean is (3 + 5 + 8 + 12 + 17) ÷ 5 = 9. The distances from the mean are 6, 4, 1, 3 and 8, which add up to 22, so the MAD is 22 ÷ 5 = 4.4. For the standard deviation, the squared distances are 36, 16, 1, 9 and 64, which add up to 126. The population variance is 126 ÷ 5 = 25.2 and the standard deviation is √25.2 ≈ 5.0200. The standard deviation is a little larger than the MAD, because it gives more weight to the large distances.
Example 5: What one extreme value does
Start with 10, 12, 14, 16, 18. Then change the last value from 18 to 48. Compare the measures of spread.
Answer: the MAD around the mean jumps from 2.4 to 11.2, but the median absolute deviation stays at 2.
Original data: the mean is 14, the distances are 4, 2, 0, 2 and 4, and they add up to 12, so the MAD is 12 ÷ 5 = 2.4. With 48 instead of 18: the mean becomes 20, the distances are 10, 8, 6, 4 and 28, and they add up to 56, so the MAD is 56 ÷ 5 = 11.2. If you measure around the median (14) instead, the distances are 4, 2, 0, 2 and 34, which add up to 42, so the MAD is 42 ÷ 5 = 8.4. For the median absolute deviation, the distances from the median are 0, 2, 2, 4 and 4 for the original data, and 0, 2, 2, 4 and 34 for the changed data. The median of each list is 2, so the median absolute deviation does not change at all.
Example 6: Same mean, different spread
Set A is 48, 49, 50, 51, 52. Set B is 30, 40, 50, 60, 70. Both have a mean of 50. Compare their MAD.
Answer: Set A has a MAD of 1.2 and Set B has a MAD of 12, so Set B is ten times more spread out.
Set A: the distances from 50 are 2, 1, 0, 1 and 2, which add up to 6, so the MAD is 6 ÷ 5 = 1.2. Set B: the distances are 20, 10, 0, 10 and 20, which add up to 60, so the MAD is 60 ÷ 5 = 12. The two sets have the same average, but the MAD shows clearly that the values in Set B are much further from it.
Example 7: Decimal values, mean or median
Find the MAD of 1.5, 2.5, 3.5, 4.5 and 8, around the mean and around the median.
Answer: the MAD around the mean is 1.8, and the MAD around the median is 1.7.
The sum is 20 and the mean is 20 ÷ 5 = 4. The distances from the mean are 2.5, 1.5, 0.5, 0.5 and 4, which add up to 9, so the MAD is 9 ÷ 5 = 1.8. The median is 3.5. The distances from the median are 2, 1, 0, 1 and 4.5, which add up to 8.5, so the MAD is 8.5 ÷ 5 = 1.7. The two results are close, because the data has only one large value.
Common mistakes when finding the MAD
A common mistake is leaving the minus signs in, which makes the distances cancel out. Another is mixing up the mean absolute deviation with the median absolute deviation, which are different measures. Also check whether your textbook measures the distances around the mean or around the median. For the simplest measure of spread, try our Range Calculator.
Created by Sajid Ali, SmartStatCalc · Last updated: 8 November 2026
Found a mistake or have a suggestion? Contact us.
How to Use Our Mean Absolute Deviation Calculator
- Type or paste your numbers into the Data Values box.
- Choose whether to measure the deviation around the mean or the median.
- Click the Calculate MAD button.
- Read the MAD, the center and the sum of the absolute deviations.
- Check the table and the step-by-step solution to see how each value contributes.
Click Reset at any time to clear your data and start again.
Why Use SmartStatCalc?
SmartStatCalc is built to make everyday statistics quick and easy to understand. Instead of working out every distance by hand, you can enter your data and see a clear result right away.
Who Can Use a Mean Absolute Deviation Calculator?
Students meet the mean absolute deviation in school and college statistics, and teachers use it to explain spread in a simple way. Analysts also use it to describe how much values such as prices, scores or measurements vary.
Frequently Asked Questions
What is the mean absolute deviation in simple words?
It is the average distance of the values from the center of the data.
What is the formula for the mean absolute deviation?
Add the absolute differences between each value and the mean, then divide by the number of values.
Why do we use absolute values?
Without absolute values, the distances above and below the mean would cancel out and add up to zero.
Is the mean absolute deviation the same as the standard deviation?
No. The standard deviation squares the distances, so it gives more weight to values far from the mean. The two are usually close but not equal.
Is it the same as the median absolute deviation?
No. The median absolute deviation is the median of the absolute distances from the median. Our calculator shows both.
Can the mean absolute deviation be zero?
Yes, but only when all values are the same.
Can the MAD be negative?
No. It is an average of distances, which are never negative.
Is this Mean Absolute Deviation Calculator free?
Yes. SmartStatCalc's Mean Absolute Deviation Calculator is free to use online.
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If you use this calculator in your work, you can cite it like this:
SmartStatCalc. (2026). Mean Absolute Deviation Calculator. https://smartstatcalc.com/mean-absolute-deviation-calculator/