What this calculator does
The midrange is the average of the minimum and the maximum, and nothing else in the data affects it. For 12, 18, 9, 25, 14, 30, 7 the minimum is 7 and the maximum 30, giving a midrange of 18.5.
That is both its appeal and its problem. It is the quickest measure of centre to compute by hand, but it uses only two values and discards the rest, which makes it the least robust of all the common centre measures. A single extreme value moves it as much as it moves the maximum.
The formula
The minimum and maximum are found and averaged. Every other value is ignored, so a data set of a thousand points contributes exactly two numbers to the result. This makes the midrange fast to compute but highly sensitive to outliers, more so than the mean and far more so than the median.
| Term | Meaning |
|---|---|
| Midrange | The average of the smallest and largest values. |
| Range | The difference between them, which is a measure of spread rather than centre. |
| Robustness | How little a statistic is affected by extreme values. The midrange has the least of any common measure. |
| Breakdown point | The share of the data that can be corrupted before a statistic becomes arbitrary. For the midrange it is zero. |
The inputs explained
| Field | What to enter |
|---|---|
| Data set (comma separated) | Your data, comma separated. Only the smallest and largest values affect the result. |
When to use it
Quick estimation
When a rough centre is needed from a glance at a range, the midrange is the fastest thing to compute.
Reporting temperature
The daily mean temperature in many meteorological records is the midrange of the daily high and low, since those two figures are what gets recorded.
Teaching measures of centre
Comparing the midrange with the mean and median on the same data shows clearly what robustness means.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the midrange compare across data sets?
Including one where a single extreme value dominates.
| Data set | Midrange | Minimum | Maximum |
|---|---|---|---|
| 10, 20, 30, 40, 50 | 30.000 | 10 | 50 |
| 12, 18, 9, 25, 14, 30, 7 | 18.500 | 7 | 30 |
| 1, 2, 3, 4, 100 | 50.500 | 1 | 100 |
Questions
What is the midrange used for?
Mostly for quick estimation and in contexts where only the extremes are recorded. Daily mean temperature in many climate records is the midrange of the high and low, because those are the two figures historically logged. It is rarely the right choice when the full data is available.
Why is the midrange not robust?
Because it uses only the two most extreme values, which are exactly the ones most likely to be outliers or errors. Its breakdown point is zero: corrupting a single observation can move it arbitrarily far. The median, by contrast, tolerates up to half the data being corrupted.
When is the midrange better than the mean?
For a symmetric distribution with short tails, such as a uniform distribution, the midrange is actually a more efficient estimator of the centre than the mean. That is a narrow case, and outside it the mean or median is almost always preferable.
Is the midrange the same as the median?
No, and they can differ enormously. The median is the middle value when sorted and depends on the ordering of every point; the midrange is the average of the two extremes and ignores everything between. They coincide only when the data happens to be symmetric.
For the middle value instead, see the median calculator. For the spread between extremes, see the range calculator.