Calcylator
Range

Range of a data set:
maximum minus minimum

Find the spread of any list of numbers with one subtraction, and learn why a single outlier can distort it.

Calcylator Editorial Team

Updated · 6 min read

What is the range of a data set?

The range is the largest value minus the smallest value in a list. For the numbers 12, 15, 9, 22 and 18, the largest is 22 and the smallest is 9, so the range is 13. It tells you how far apart the extremes are.

Because it uses only two numbers, the range is the fastest measure of spread. It works for test scores, daily temperatures, prices, delivery times or any other list of numbers.

The range formula

Range =range = maximum − minimum
range:
spread of the data
maximum:
largest value in the list
minimum:
smallest value in the list
The Range calculator takes a list of numbers and returns max − min with up to four decimals.

  • Values

    12, 15, 9, 22, 18

  • Maximum

    22

  • Minimum

    9

Range

13

22 − 9 = 13. The order of the list does not matter.

  1. Scan the list and note the largest value.
  2. Note the smallest value.
  3. Subtract the smallest from the largest.
  4. Keep the unit of the data, for example degrees or marks.

Range and outliers: why one value matters

The range is very sensitive to extreme values. Add a single reading of 90 to the list above and the range jumps from 13 to 81, even though most numbers have not changed.

Effect of one outlier
ListMaximumMinimumRange
12, 15, 9, 22, 1822913
12, 15, 9, 22, 18, 9090981

That is why analysts often report the range beside the mean or median, or use a measure such as the standard deviation when outliers are likely.

Where the range is used

A weather page shows the daily temperature range as the high minus the low. A teacher compares the range of two classes' marks to see which group is more spread out. A shop manager looks at the range of weekly sales to understand how much they vary.

The range is also a quick data check. If a column of ages shows a range of 200, a mistake is hidden in the data. It is a first look before more detailed statistics.

A second example: weekly prices

A shop records the price of a bag of rice over five weeks: 62, 65, 61, 64 and 70 rupees. The maximum is 70 and the minimum is 61, so the range is 9 rupees. A small range like this tells the owner that the price is stable.

If the same shop recorded 62, 65, 61, 64 and 95, the range would be 34. The jump flags that something unusual happened that week, which is exactly the kind of question the range is good at raising.

Common mistakes when finding the range

  • Subtracting the first value from the last instead of the minimum from the maximum. The list does not need to be in order.
  • Reporting the range as two numbers. In statistics the range is one value: the difference.
  • Forgetting negative numbers. For values from −5 to 8 the range is 8 − (−5) = 13.
  • Using the range alone to compare groups with different sizes or obvious outliers.

Common questions

How do you find the range of a data set?

Subtract the smallest value from the largest value. For 12, 15, 9, 22 and 18, the range is 22 − 9 = 13. You do not need to sort the list first, you only need to spot the two extremes.

What is the range formula?

The range formula is range = maximum − minimum. It gives a single number showing how far apart the highest and lowest values are. The unit of the range is the same as the unit of the data.

Can the range be negative?

No. The maximum is never smaller than the minimum, so the difference is zero or more. A range of zero means every value in the list is the same. A negative answer means the two numbers were swapped.

Why is the range affected by outliers?

The range uses only the highest and lowest values, so one extreme number changes it directly. Adding 90 to a list with a range of 13 makes the range 81. Measures that use every value, such as the standard deviation, react less.

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