# How to Calculate Percentiles

When you take a test and get a score back 87%. It tells you how many questions you got right. But your test score doesn’t tell you how well you did compared to other people who took the test. Percentiles are values from 0 to 99 that tell you the percentage of tests with scores less than a particular score. If the percentile of your test score is 75, this means you scored higher than 75% of the people who took the test. Percentiles can be used to compare values in any set of data that is ordered You can compute percentiles for income, weight, and many other things. There two calculations commonly used.

#### Things You'll Need

• Data set of observations (in this guide, we will assume a set of 150 test scores)
• Calculator
• Computer spreadsheet or pencil and paper for sorting the data set

## Instructions

• 1

Sort the test scores so they are in order from lowest to highest score. Normally this is done by entering the scores in a computer spread sheet and then clicking on the sort command. You can do this manually by listing the possible scores on the test in order and then making a hash mark beside the appropriate score for each test.

• 2

Start to calculate the percentile of your test score (as an example we’ll stick with your score of 87). The formula to use is L/N(100) = P where L is the number of tests with scores less than 87, N is the total number of test scores (here 150) and P is the percentile. Count up the total number of test scores that are less than 87. We’ll assume the number is 113. This gives us L = 113 and N = 150.

• 3

Divide out L/N to get the decimal equivalent. (113/150 = 0.753). Multiply this by 100 (0.753(100) = 75.3).

• 4

Discard the digits to the right of the decimal point. For 75.3 this leaves 75. This is the percentile of a score of 87 and means you did better than 75% of the people who took the test. Not bad at all!

• 5

Calculate the score which is at a given percentile. Let’s say you want to know what the median test score is (the test score for which 50% of the students scored less and 50% scored as much or higher. We use the same variables but a slightly different equation. The formula is P/100(N) = L. In our example, P = 50 and N = 150 so we have 50/100(150) = 75.

• 6

Count the number of test scores starting with the lowest until you get to 75. The next higher score (#76) is the score at the 50th percentile.

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