Range Calculator — largest minus smallest

How it works

The range is the simplest measure of spread. As the NIST/SEMATECH e-Handbook puts it, "the range is the largest value minus the smallest value in a data set":

range = maximum − minimum

It tells you the full width the data covers, but because it uses only the two extreme values, it says nothing about how the values in between are distributed — and a single outlier can inflate it. For a fuller picture of spread, pair it with the standard deviation.

The calculator also reports the midrange, the average of the smallest and largest values ((min + max) ÷ 2), plus the sum and count of your data.

Worked example

For 2, 4, 4, 4, 5, 5, 7, 9: the largest value is 9 and the smallest is 2, so the range is 9 − 2 = 7. The midrange is (2 + 9) ÷ 2 = 5.5, the sum is 40, and there are 8 values.

Frequently asked questions

How do you find the range of a data set?

Identify the largest and smallest values and subtract: range = maximum − minimum. For 2, 4, 4, 4, 5, 5, 7, 9 the range is 9 − 2 = 7.

What is the midrange?

The midrange is the average of the minimum and maximum, (min + max) ÷ 2. For the set above it is (2 + 9) ÷ 2 = 5.5. It marks the center of the data's full span.

Why is the range a limited measure of spread?

Because it depends only on the two extreme values, it ignores how the rest of the data is distributed and is very sensitive to outliers. The standard deviation, which uses every value, is a more robust measure.

Does the range work with negative numbers and decimals?

Yes. It is still maximum minus minimum. For −3, 1.5, 4, −0.5 the range is 4 − (−3) = 7.

What is the range if all values are the same?

Zero. When every value is identical the maximum equals the minimum, so their difference is 0.

How is the range different from the interquartile range?

The range spans all the data (max − min); the interquartile range (IQR) spans just the middle 50% (Q3 − Q1), which ignores the extremes and so resists outliers.