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Percentile Rank in Statistics: Definition & Formula

Percentile Rank in Statistics: Definition & Formula
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  • 1:00 Formula for Percentile Ranks
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Lesson Transcript
Instructor: Chris Clause
In this lesson, you will learn to define percentile rank and learn how it is calculated. Following this lesson, you will have the opportunity to test your knowledge with a short quiz.

What is Percentile Rank?

In the world of statistics, percentile rank refers to the percentage of scores that are equal to or less than a given score. Percentile ranks, like percentages, fall on a continuum from 0 to 100. For example, a percentile rank of 35 indicates that 35% of the scores in a distribution of scores fall at or below the score at the 35th percentile.

Percentile ranks are useful when you want to quickly understand how a particular score compares to the other scores in a distribution of scores. For instance, knowing someone scored 235 points on an exam doesn't tell you much. You don't know how many points were possible, and even if you did, you wouldn't know how that person's score compared to the rest of his classmates. If, however, you were told that he scored at the 90th percentile, then you would know that he did as well or better than 90% of his class.

Formula for Percentile Ranks

The formula for calculating percentile ranks is relatively simple and straightforward. Knowing only the distribution of scores, you can easily calculate the percentile rank for any of the scores in the distribution. The percentile rank formula is: R = P / 100 (N + 1). R represents the rank order of the score. P represents the percentile rank. N represents the number of scores in the distribution.

Let's say that you are a college professor, and one of your students, Jim, scored 78 points on his final exam. He wants to know what his percentile rank was for the test. Using the following distribution of all 20 scores you can calculate his percentile rank:

34, 37, 48, 59, 62, 75, 76, 78, 79, 80, 82, 85, 90, 91, 92, 92, 94, 97, 99, 100

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