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Midrange

M=xmax⁡+xmin⁡2M = \frac{x_{\max} + x_{\min}}{2}

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Learning zone

The midrange is the average of the two extremes, and it is the centre measure hiding in plain sight all over daily life: the "mean daily temperature" printed in climate records is almost always the midrange of the day's high and low, not the average of hourly readings. With a high of 98 and a low of 62, the midrange is 80. It is also the natural centre when data are bounded by design — the nominal size of a machined part specified as 24.8 to 25.2 mm sits at the midrange, 25.0.

Its weakness is the mirror of the range's: built from two numbers, it is the least robust centre statistic there is, with a breakdown point of zero. One typo in the maximum drags it anywhere you like, whereas the median would not budge. The classic demonstration is income data, where a single billionaire in the sample pushes the midrange into the tens of millions while the median stays put near the truth. Use it for a fast sanity check or for bounded, symmetric data, and reach for the median or mean when the answer has to survive scrutiny.

Midrange
M=xmax⁡+xmin⁡2M = \frac{x_{\max} + x_{\min}}{2}
Where
  • MM= Midrange
  • xmax⁡x_{\max}= Maximum value
  • xmin⁡x_{\min}= Minimum value
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