About the Mean Absolute Deviation Calculator
This mean absolute deviation calculator measures how spread out a data set is by averaging how far each value sits from the centre. Paste your numbers and it returns the mean absolute deviation (MAD) around the mean, the average absolute deviation around the median, and the median absolute deviation — a robust spread measure used to flag outliers — along with the scaled MAD and the sample standard deviation for comparison.
It is written for students working through middle-school and AP Statistics MAD problems, teachers who want a worked table to show the class, and analysts who need a spread measure that is easier to explain than standard deviation. Every value gets its own row showing the distance from the mean and from the median, so you can check homework line by line.
Mean absolute deviation uses absolute distances rather than squared distances, so a single extreme value pulls it up less than it pulls up the standard deviation. The median absolute deviation goes further and is almost unaffected by outliers, which makes it the better choice for skewed or messy data.
With the default inputs, the mean absolute deviation (around the mean) is 3.75. Change any value above to recalculate instantly.
How to use the mean absolute deviation calculator
- 1Paste or type your numbers, separated by commas, spaces or line breaks.
- 2Read the mean absolute deviation — the average distance from the mean.
- 3Compare it with the median absolute deviation if your data may contain outliers.
- 4Use the deviation table to check each step of a homework or exam answer.
Formula and method
The mean absolute deviation is found in three steps: compute the mean x̄, take the absolute distance of every value from that mean, then average those distances by dividing their sum by n (the number of values). Because distances are not squared, every unit of deviation counts equally, which makes MAD easy to interpret as “the typical distance from the average”.
The median absolute deviation replaces both averages with medians: find the median of the data, take each value’s absolute distance from it, and report the median of those distances. Multiplying it by 1.4826 gives the scaled MAD, a robust estimate of the standard deviation for normal data. Values more than about 3.5 scaled MADs from the median are commonly flagged as potential outliers (Iglewicz and Hoaglin’s modified z-score rule).
- xᵢ
- Each data value
- x̄
- Arithmetic mean of the data
- n
- Number of values
- |…|
- Absolute value (distance, ignoring sign)
Worked examples
Eight values from a classroom exercise
The mean of 3, 6, 6, 7, 8, 11, 15 and 16 is 72 ÷ 8 = 9. The absolute deviations are 6, 3, 3, 2, 1, 2, 6 and 7, which sum to 30, so the MAD is 30 ÷ 8 = 3.75. Around the median of 7.5 the deviations average 3.5, and their median is 2.5.
Ten test scores
The scores average 85.8. Their absolute deviations from the mean add to 50, so the typical score is 5 points from the class average. The sample standard deviation is 6.14 — larger, because squaring gives the wider gaps more weight.
One outlier in a small data set
The value 100 drags the mean up to 22 and the MAD to 31.2. The median absolute deviation is only 1 because the median (3) and most distances from it are unaffected by the outlier, which is why it is preferred for robust outlier detection.
Frequently asked questions
How do you find the mean absolute deviation?+
Find the mean of the data, subtract the mean from each value and drop any minus signs, add up those absolute deviations, and divide by the number of values. The result is the average distance of the data from its mean.
What does the mean absolute deviation tell you?+
It tells you how far, on average, values are from the mean. A small MAD means the data are tightly clustered around the average; a large MAD means they are spread out. It is in the same units as the data, so a MAD of 5 points means scores are typically 5 points from the average.
What is the difference between mean absolute deviation and standard deviation?+
Both measure spread, but standard deviation squares each deviation before averaging and then takes a square root, which gives large deviations extra weight. MAD averages plain distances, so it is smaller and less sensitive to outliers. For normal data, MAD is roughly 0.8 times the standard deviation.
What is the median absolute deviation?+
It is the median of the absolute distances from the median. Because it uses medians twice it is extremely resistant to outliers. Multiplying it by 1.4826 gives an estimate of the standard deviation for normally distributed data, and it is used in modified z-scores to flag outliers.
Is MAD the same for a sample and a population?+
Yes. Unlike variance and standard deviation, the mean absolute deviation is normally computed by dividing by n in both cases; there is no n − 1 correction in the standard definition taught in schools and used by most software.