The midrange is the simplest possible measure of the centre of a data set: the average of its two most extreme values. It is the midpoint of the interval that the data cover, so it tells you where the centre of that interval lies. Weather reports use it implicitly when they quote the average of the daily high and low temperature.
Its simplicity is also its weakness. Because only the minimum and maximum enter the formula, a single unusual value moves the midrange by half of its own error, and the bulk of the data has no influence at all. For data with outliers or skew the median or mean is a much better summary. For data that are known to be evenly spread between two limits (a uniform distribution) the midrange is, however, a surprisingly efficient estimate of the centre.
Enter your numbers – in any order – and the calculator picks out the extremes, computes the midrange and compares it with the mean and median, which is a quick way to see whether one tail of the data is longer than the other.
How to use the Midrange Calculator
- Data set
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How it works
Find the minimum and maximum of the data, add them and divide by two.
Worked example
Six temperatures: 14, 22, 9, 31, 18, 27 °C. The minimum is 9 and the maximum is 31, so the midrange = (9 + 31) ÷ 2 = 20 °C and the range is 22. The mean is 121 ÷ 6 ≈ 20.17 and the median is (18 + 22) ÷ 2 = 20, so here all three measures agree closely – a sign of roughly symmetric data. If the 31 were a faulty 61, the midrange would jump to 35 while the median would stay at 20.
When to use the midrange
- Quick mental estimates (daily mean temperature from high and low).
- Data known to be spread evenly between two limits.
- Not for data with outliers or a long tail – use the median there.
Formula
Midrange = (minimum + maximum) ÷ 2 · Range = maximum − minimum
Worked example
Inputs — Data set: 14, 22, 9, 31, 18, 27.
Results — Midrange = 20; Minimum = 9; Maximum = 31; Range = 22; Mean (for comparison) = 20.1667; Median (for comparison) = 20.
Key terms
- Midrange
- (minimum + maximum) ÷ 2, also called the mid-extreme.
- Range
- maximum − minimum.
- Extremes
- The smallest and largest values of a data set.
Frequently asked questions
What is the midrange?
The average of the minimum and maximum values, (min + max) ÷ 2.
What is the midrange of 14, 22, 9, 31, 18, 27?
The minimum is 9 and the maximum is 31, so the midrange is (9 + 31) ÷ 2 = 20.
Is the midrange the same as the median?
No. The median is the middle of the sorted values; the midrange is the middle of the interval they cover. They coincide only for symmetric data.
Is the midrange a good measure of centre?
Only for data without outliers; one extreme value shifts it substantially.
What is the difference between range and midrange?
The range (max − min) measures spread; the midrange ((max + min) ÷ 2) measures centre.
Can the midrange be negative?
Yes, if the minimum is more negative than the maximum is positive, e.g. −10 and 4 give −3.