# Midrange

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The midrange is infrequently used and hardly known. It is a relatively straight-forward measure of central tendency.

It is merely the arithmetic mean amongst the data subset including only the minimum and maximum values of the larger set, ignoring all intermediate values of the set. In other words, it is the arithmetic average of strictly the minimum and maximum values of the set.

Midrange = $\frac{\mathrm{Min(x)} + \mathrm{Max(x)}}{2}$

The midrange is the central point of the possible values that were taken, assuming that the minimum and maximum are the only possible extremes. This is much like the arithmetic mean, except takes into account the possibility that some intermediate value were possible though not observed (while the arithmetic mean only includes the values actually observed). In other words, the midrange takes into account the zero-values that exist between minimum and maximum as coincidental, and assumes the possibilities of values collected evenly spaced.

The disadvantage of the midrange, however, is the fact that it fails to weight the data collected. It's an unweighted average, so to speak.