Intervals are used in mathematics for a variety of reasons. An interval is a specific segment of a data set. For example, an interval might be from 4 to 8. Intervals are used in statistics and in calculus when deriving integrals. Intervals are also used when attempting to find the mean from frequency tables. The midpoint of each interval is needed to complete this process and find the mean.

Find the upper and lower limit of the interval. For example, an interval from 4 to 8 would have 4 as the lower limit and 8 as the upper limit.

Sum the upper and lower limit. In the example, 4 + 8 = 12.

Divide the sum of the upper and lower limits by 2. The result is the midpoint of the interval. In the example, 12 divided by 2 yields 6 as the midpoint between 4 and 8.

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