Range Calculator

Range, minimum, maximum and the range rule of thumb for standard deviation.

Range = largest value − smallest value. For 4, 9, 2, 15, 7 the range is 15 − 2 = 13. The range rule of thumb estimates the standard deviation as range ÷ 4, here about 3.25.

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How to use it

  1. Paste or type your numbers, separated by commas, spaces or new lines.
  2. Read the range, minimum, maximum and midrange.
  3. Compare the range rule of thumb estimate with the real standard deviation.

What you enter

What you get

Formula

Range = max − min | Midrange = (max + min) ÷ 2 | s ≈ range ÷ 4

Worked example

Input: 4, 9, 2, 15, 7

Result: Range 13, min 2, max 15, midrange 8.5

The data spread over 13 units.

Questions

How do you find the range in math?

Find the largest and smallest values in the data set and subtract the smallest from the largest.

Can the range be negative?

No. The maximum is always at least as large as the minimum, so the range is zero or positive.

What is the range rule of thumb?

A quick estimate of standard deviation: s ≈ range ÷ 4. It works best for roughly bell-shaped data with about 30 or more values.

Why is the range sensitive to outliers?

It uses only the two most extreme values, so a single outlier changes it. The interquartile range is more robust.

Limitations

References

Related reading

More Statistics

All free tools · By Dr. Zubair Khalid, DVM, MS, PhD.