To calculate the Mean Absolute Deviation (MAD), follow these steps:
- Calculate the mean (average) of the data set : Add all the data values and divide by the number of values.
Mean=∑data valuesn\text{Mean}=\frac{\sum \text{data values}}{n}Mean=n∑data values
- Find the absolute deviations : Subtract the mean from each data value and take the absolute value (ignore negative signs).
Absolute Deviation=∣xi−xˉ∣\text{Absolute Deviation}=|x_i-\bar{x}|Absolute Deviation=∣xi−xˉ∣
where xix_ixi is each data value and xˉ\bar{x}xˉ is the mean.
- Sum the absolute deviations : Add all the absolute deviations together.
- Calculate the mean absolute deviation : Divide the sum of absolute deviations by the number of data values.
MAD=∑∣xi−xˉ∣n\text{MAD}=\frac{\sum |x_i-\bar{x}|}{n}MAD=n∑∣xi−xˉ∣
This gives the average distance of each data point from the mean, indicating the variability in the data set
Example
For data set: 302, 140, 352, 563, 455, 215, 213
- Mean = (302 + 140 + 352 + 563 + 455 + 215 + 213) / 7 = 320
- Absolute deviations = |302 - 320|, |140 - 320|, |352 - 320|, |563 - 320|, |455 - 320|, |215 - 320|, |213 - 320|
- Sum of absolute deviations = 18 + 180 + 32 + 243 + 135 + 105 + 107 = 820
- MAD = 820 / 7 ≈ 117.14
So, the mean absolute deviation is approximately 117.14
. This method works similarly for grouped data, where frequencies are considered in the calculation
