Mean Absolute Deviation (MAD) Calculator
Enter a list of numbers and instantly get the mean absolute deviation (MAD), mean, median, range, and standard deviation — with a bar chart showing each value's contribution.
Average of |xᵢ − mean| across all values
- 1
Count n
8 - 2
Mean x̄ = Σxᵢ / n
Σxᵢ ÷ 8 = 5 - 3
Σ|xᵢ − x̄|
12Sum of each value's absolute distance from the mean. - 4
MAD = Σ|xᵢ − x̄| / n
12 ÷ 8 = 1.5000
此計算機如何運作？
MAD = Σ|xᵢ − x̄| / n — compute the mean, find each value's absolute distance from the mean, then average those distances. For {2,4,4,4,5,5,7,9}: mean = 5, MAD = 1.5. MAD is more intuitive than standard deviation and less sensitive to outliers because it uses absolute values instead of squares.
公式
How this is calculated
The mean absolute deviation (MAD) measures how spread out data values are from their mean. First, compute the arithmetic mean x̄ = Σxᵢ / n. Then compute the absolute difference between each value and the mean: |xᵢ − x̄|. Finally, average those absolute differences: MAD = Σ|xᵢ − x̄| / n. A MAD of 0 means all values are equal; a larger MAD indicates more spread.
MAD is often preferred over standard deviation as an introductory measure of spread because it avoids squaring — the absolute value is more intuitive and less sensitive to extreme outliers than the squared terms in variance. For the classic data set {2, 4, 4, 4, 5, 5, 7, 9}, the mean is 5 and the MAD is (3+1+1+1+0+0+2+4)/8 = 12/8 = 1.5.
The calculator also reports population standard deviation (σ = √(Σ(xᵢ−x̄)²/n)) for comparison. Note that this calculator uses the population formula (dividing by n), not the sample formula (dividing by n−1). Use n−1 when the data is a sample drawn from a larger population and you want an unbiased estimate of the population standard deviation.
常見問題
Both measure spread from the mean. MAD averages the absolute deviations |xᵢ − x̄|, while standard deviation averages squared deviations and then takes the square root. Squaring penalises outliers more heavily, making standard deviation larger and more sensitive to extreme values than MAD.
Use MAD when explaining spread to a non-technical audience (the meaning is more intuitive), when the data contains significant outliers (MAD is more robust), or in fields like economics and signal processing where absolute deviations are more interpretable than squared ones.
No — MAD and all the reported statistics are order-independent. {2, 4, 5} gives the same result as {5, 2, 4}. The bar chart displays values in the order you entered them so you can cross-reference each bar with its position in your data.
也稱為
TG we-Calculate Editorial Team. (2026). Mean Absolute Deviation (MAD) Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/zh-tw/calculator/mad-calculator
TG we-Calculate Editorial Team. "Mean Absolute Deviation (MAD) Calculator." TG we-Calculate. 2026. https://we-calculate.com/zh-tw/calculator/mad-calculator.
TG we-Calculate Editorial Team, "Mean Absolute Deviation (MAD) Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/zh-tw/calculator/mad-calculator
@misc{wecalculate_mad_calculator, title = {Mean Absolute Deviation (MAD) Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/zh-tw/calculator/mad-calculator}}, year = {2026}, note = {TG we-Calculate} }
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