How to Compute Percentiles on a Histogram

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A histogram is a graph of a single continuous variable. The variable is first categorized into bins. Then these bins are listed on the x (horizontal) axis. Then a rectangle is placed over the bin, the height of which is proportional to the frequency of the bin.
The percentiles of a distribution are the values that separate the variable into 100 groups of equal frequency.

    Find the frequency of each bin. You can do this by drawing a horizontal line from the top of each rectangle to the y-axis (the vertical axis) and finding the frequency. You may need to estimate this, if the line is between two tick marks.
    Suppose you have a histogram with 5 bins, and the frequencies are 5, 15, 20, 7 and 3.

    Add the frequencies found in step 1. In the example, the total is 5 + 15 + 20 + 7 + 3 = 50.

    Divide the frequency for each bin by the total frequency. In the example: 5/50, 15/50, 20/50, 7/50 and 3/50.

    Divide 100 by the total frequency. In the example 100/50 = 2.

    Multiply the numerator (top part) of each fraction in step 3 by the quotient in step 4. In the example 5_2 = 10, 15_2 = 30, 20_2 = 40, 7_2 = 14 and 3*2 = 6.

    Sum the results cumulatively. That is, add the first two numbers, the first three and so on until you have added them all. These are the percentiles for upper number in each bin. In the example: 10, 10 + 30 = 40, 40 + 40 = 80, 80 + 14 = 94 and 94 + 6 = 100.

    Warnings

    • The histogram is not really intended for finding percentiles, and you will often have to approximate.

References

About the Author

Peter Flom is a statistician and a learning-disabled adult. He has been writing for many years and has been published in many academic journals in fields such as psychology, drug addiction, epidemiology and others. He holds a Ph.D. in psychometrics from Fordham University.

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