Mean Absolute Deviation (MAD) Calculator
Use this unified calculator to find the mean absolute deviation (MAD) for both ungrouped (raw) data and grouped (frequency distribution) data. MAD measures the average distance of observations from the mean.
Quick Start
| Mean Absolute Deviation Calculator | |
|---|---|
| Data Type | Ungrouped (Raw Data) Grouped (Frequency Distribution) |
| Enter the X Values (Separated by comma,) | |
| Type of Frequency Distribution | DiscreteContinuous |
| Enter the Classes for X (Separated by comma,) | |
| Enter the frequencies (f) (Separated by comma,) | |
| Results | |
| Number of Observations (N): | |
| Sample Mean: | |
| Mean Absolute Deviation (MAD): | |
Understanding Mean Absolute Deviation
MAD measures the average absolute distance of observations from the mean:
- Simpler than variance (no squaring)
- Easier to interpret (same units as original data)
- Less sensitive to extreme outliers than standard deviation
- All deviations count equally (no weighting by magnitude)
Formula
Ungrouped Data: $$MAD = \frac{1}{n}\sum_{i=1}^{n}|x_i - \overline{x}|$$
Grouped Data: $$MAD = \frac{1}{N}\sum_{i=1}^{k}f_i|x_i - \overline{x}|$$
Worked Examples
Example 1: Ungrouped Data
Data: 10, 15, 20, 25, 30
Mean = 20
|Value | |x - 20| | |—|—| | 10 | 10 | | 15 | 5 | | 20 | 0 | | 25 | 5 | | 30 | 10 | | Total | 30 |
$$MAD = \frac{30}{5} = 6$$
Example 2: Grouped Data
Data: Values 2,3,4 with frequencies 5,8,7
Mean = 2.8
$$MAD = \frac{5|2-2.8| + 8|3-2.8| + 7|4-2.8|}{20} = \frac{4+1.6+8.4}{20} = 0.7$$
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