StatReason

Range Calculator

Enter a list of numbers to find the distance between the smallest and largest values.

Separate values with commas, spaces, tabs, or one per line.

What this answers

The range answers "how far apart are the smallest and largest values in this data?" It is the simplest possible measure of spread: one subtraction, using only the two most extreme observations and ignoring everything in between.

How it is calculated

Range is the maximum value minus the minimum value. That is the entire calculation. No other value in your dataset affects the result at all, which is exactly what makes the range fast to compute and easy to misuse: a single unusually extreme value can make the range look dramatic even if every other value clusters tightly together.

Worked example

For the values 2, 5, and 9: the maximum is 9 and the minimum is 2, so the range is 9 minus 2, which is 7. Notice that the middle value, 5, plays no role whatsoever in this result. Two completely different datasets sharing the same min and max would report the identical range even if their internal spread looked nothing alike.

Assumption audit

Calculated from your data: the count of values and the two extreme values (minimum and maximum) that determine the range.
Evidence to review: whether the minimum or maximum look like genuine extreme values worth a closer look, since the range is entirely driven by these two points and nothing else in your data.
You must verify: that the minimum and maximum are both valid, correctly measured observations, not data-entry mistakes, since the range cannot distinguish a genuine extreme value from an error.

Common mistakes

Treating the range as a complete description of spread is the most common mistake: because it depends only on two points, it is highly sensitive to a single unusual value and tells you nothing about how the rest of the data is distributed. The interquartile range or standard deviation give a fuller picture by using more of your data.

Limitations

The range grows automatically as sample size grows, purely because a larger sample is more likely to include a more extreme value by chance, not because the underlying spread actually changed. It is best used as a quick, rough check, not a rigorous spread measure.