Dispersion measures how widely dispersed the data points of a data set are. Standard deviation is heavily influenced by extreme outliers that in turn affect the average. Mean absolute deviation is based on the median, which can provide a measure of the core data without being affected by a few extreme data points. According to “Business Statistics” by Naval Bajpai, the median absolute deviation (MAD) provides an absolute measure of dispersion not affected by extreme outliers that can throw off statistical analysis based on means and standard deviations.

## Calculating Median

List all of the observations in the data set from smallest to largest. If a number occurs more than once, list it the same number of times as it occurs.

Count the number of observations.

Divide the number of observations by 2. If there are an odd number of observations and thus they cannot be evenly divided by, the middle observation is the median. Otherwise, this average of the two middle numbers is the halfway point.

Take the two observations that are just above and below the halfway point. Then average these two observations. This value is the median.

## Calculating Median Absolute Deviation

Subtract each value in the data set from the median. This gives the deviation of each data point from the median.

Total up all of the deviations for the data set. This can be sped up by using a calculator.

Divide the total for all of the deviations for the data set by the number of observations. The result is the median absolute deviation.

#### Tips

According to the book, “Practical Statistics for the Analytical Scientist,” while MAD is not an estimate of standard deviation, if the data distribution is approximately normal, multiplying MAD by 1.483 provides an approximate estimation of standard deviation.

#### Warnings

Median-based statistics cannot be used in six sigma quality-based statistics.

#### References

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