Question

This is known as the mean absolute deviation (MAD).

a. Press "Play" to see how to calculate the mean absolute deviation.



b. Explain how to calculate the mean absolute deviation in your own words

Answer 1

Here’s a simple way to calculate the mean absolute deviation (MAD) in your own words, followed by a short example.

Steps
1. List your data and find the mean (average) of the data.
2. For each data point, subtract the mean to get its deviation.
3. Take the absolute value of each deviation (so negatives don’t cancel positives).
4. Add up those absolute deviations.
5. Divide that sum by the number of observations. The result is the MAD — the average distance of the data points from the mean.

Quick example
Data: 2, 4, 6, 8
1. Mean = (2+4+6+8)/4 = 5
2. Deviations: 2−5 = −3, 4−5 = −1, 6−5 = 1, 8−5 = 3
3. Absolute deviations: 3, 1, 1, 3
4. Sum = 8
5. MAD = 8 / 4 = 2

Notes
- MAD measures typical distance from the mean; it’s always nonnegative.
- If your data include frequencies, use the weighted sum of absolute deviations divided by total frequency.
- There’s also the median absolute deviation (uses the median instead of the mean) if you want a more robust measure against outliers.