Get the mean absolute deviation (MAD): the average distance of each value from the mean, with a distance table.
Separate numbers with commas, spaces or line breaks. You can paste a column from Excel or Sheets. 7 values read.
| Mean | 10.2857 |
|---|---|
| Median absolute deviation | 4 |
| Standard deviation (population), for comparison | 8.6473 |
| x | x − x̄ | |x − x̄| |
|---|---|---|
| 2 | −8.2857 | 8.2857 |
| 4 | −6.2857 | 6.2857 |
| 6 | −4.2857 | 4.2857 |
| 8 | −2.2857 | 2.2857 |
| 10 | −0.2857 | 0.2857 |
| 12 | 1.7143 | 1.7143 |
| 30 | 19.7143 | 19.7143 |
| Σ|x − x̄| | 42.8571 | |
MAD = 42.8571 ÷ 7 = 6.12245
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MAD = Σ|x − x̄| ÷ n
It answers the most natural question about spread: on average, how far is a value from the mean? Compare it with the standard deviation, which answers a slightly different question by squaring first. In the example 2, 4, 6, 8, 10, 12, 30, the value 30 adds 20 to the MAD total but 400 to the sum of squares, which is why the SD reacts more to outliers.
Find the mean. Subtract it from each value and drop the minus signs (take absolute values). Add those distances and divide by how many values there are.
Squaring gives big deviations extra weight, so the standard deviation is always at least as large as the MAD. For normal data the MAD is about 0.8 times the SD.
Both are abbreviated MAD. The mean absolute deviation averages distances from the mean. The median absolute deviation takes the median of distances from the median, which makes it highly resistant to outliers. Check which one your course means; this page shows both.
It appears in US Common Core Grade 6 and 7 statistics as a first measure of spread before standard deviation, because it avoids squares and square roots.