The mean deviation (also called average deviation), of a set of N numbers X₁,X₂,...,X_N is abreviated by MD and is defined by

where is the arithmetic mean of the numbers and is the absolute value of the deviation of X_j from

Properties:

• The mean deviation is based on all the observations.
• Shows the dispersion of values around the measure of central tendency.
• It is easy to compute.
• Average deviation from mean is always zero in any data set. The MD avoids this problem by using absolute values to elimitate negative signs.
• The mean deviation is a better measure of absolute dispersion than the range and the quartile deviation.

Occasionally the mean deviation is defined in terms of absolute deviations from the median or other average instead of from the mean:

• When the mean deviation is calculated about the median, the formula becomes:

• When the mean deviation is calculated about the mode, the formula becomes: