平均绝对偏差计算器
计算数据点与均值之间的平均绝对偏差。
Mean Absolute Deviation
3.0000
Mean Absolute Deviation vs Value 1
公式
How to Calculate Mean Absolute Deviation
Formula
MAD = (1/n) * Sum of xi - mean
For each value, find the absolute difference from the mean, then average those differences. Unlike variance, MAD does not square the deviations, making it less sensitive to outliers and easier to interpret: it is literally the average distance from the mean.
计算示例
Find the MAD of 3, 6, 9, 12.
- 01Mean = (3 + 6 + 9 + 12) / 4 = 30 / 4 = 7.5
- 02Absolute deviations: |3-7.5|=4.5, |6-7.5|=1.5, |9-7.5|=1.5, |12-7.5|=4.5
- 03Sum of absolute deviations = 4.5 + 1.5 + 1.5 + 4.5 = 12
- 04MAD = 12 / 4 = 3
常见问题
How does MAD differ from standard deviation?
MAD uses absolute deviations while SD uses squared deviations. MAD is more robust to outliers and easier to interpret, but SD has nicer mathematical properties for theoretical statistics.
Is MAD always smaller than standard deviation?
For most distributions, yes. For a normal distribution, MAD ≈ 0.7979 * SD. Squaring in SD amplifies large deviations, making SD generally larger.
When should I use MAD?
Use MAD when you want a robust, easily interpretable measure of spread, especially if outliers are present or the distribution is non-normal.
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