How to Find the Range of Numbers

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When analyzing data sets in pre-statistics courses, you may often need to find the range of the numbers of a given set. The value of the range indicates the degree of variety within the data set. It is a common math problem that students may encounter on many standardized tests. Once you know what the mathematical definition of range is, you can use a simple mathematical operation to solve this type of problem.

    Know that to compute the range of numbers of a data set you must subtract the smallest number value from the largest number value in the set. The range is simply the difference of these two numbers and indicates how spread apart the data set is. Note that the data set is just the list of numbers.

    Order the numbers given in a data set from the smallest to greatest value to facilitate the calculation. As an example, use the data set with the numbers 10, 8, 11, 12, 1, 3, 1, 4, 6 and 5. Arrange these numbers in ascending order to get 1, 1, 3, 4, 5, 6, 8, 10, 11 and 12.

    Locate the smallest and largest numbers of the data set. For the example given in Step 2, these numbers are 1 and 12 respectively.

    Calculate the range of the data set by subtracting the smallest from the largest number given in Step 3. The range for the example is 12 - 1 = 11.

    Practice the method outlined in Step 2 through Step 4 to find the range of the following test scores: 55, 60, 75, 80, 85, 90 and 100. Since the scores are already in order from the smallest to greatest score, you subtract 55 from 100 to get 45 as the range for this data set.

    Things You'll Need

    • Paper
    • Pencil


    • When the numbers in the data set are very spread out, the range will tend to be large. (See Reference 2)

      Besides the term statistical range, some other terms associated with the analysis of data sets are mean, median and mode. (See Resource 1)

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