How to find percentile, percentile rank and percentile range

By Indeed Editorial Team

Published 4 July 2022

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

Percentile rank is a common statistical measurement that may apply to several types of problems, including exam scores, weight analysis and age distribution within a sample group. Statisticians might use percentile rank to understand how a particular value, like a test score, compares to other values in a given set, like the scores of other test-takers. Professionals and students often use percentile rank to get a better insight into how well they performed on an assessment when juxtaposed with other candidates, guiding future study goals.

In this article, we discuss some key methods for calculating percentile rank, provide detailed examples and explore related concepts.

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How to find a percentile

Before calculating percentile rank, you first want to find the percentile of the particular item you're working with. You might locate the percentile of a specific score using this formula:

Percentile = (number of values below score) ÷ (total number of scores) x 100

Consider the following example:

A student scores 1,400 points out of 1,600 on an exam. The student may use the percentile formula shown above to find out how that score compares with that of other test-takers. To get the percentile rank, they might begin by gathering certain information about the data set, which, in this case, is the other test-takers' data.

The steps below outline how to calculate the percentile using example test scores:

1. Arrange the data in ascending order

When calculating the percentile of a data set such as test scores, organise the values in ascending order. You start with the lowest value and end with the highest.

Example: The data set of standardised test scores for all the test-takers is 77, 76, 88, 85, 87, 78, 82, 99, 90, 83, 89, 92, 75, 73, 62. The student who wants to find their percentile has a score of 88. The values in this data set, arranged in ascending order are 62, 73, 75, 76, 77, 78, 82, 83, 85, 87, 88, 89, 90, 92, 99.

2. Divide

Once you've placed the values in ascending order, you count the number of values that occur below your target score. You then divide this number by the total number of values you're working with.

Example: Using the data set scores from the previous section and the student's score of 88, you find that the number of values below 88 is 10. They then proceed by counting all the values in the data set, which is 15 different scores. They plug these values into this formula:

Percentile = (number of values below score) / (total number of scores) x 100

(10) / (15) x 100

3. Multiply the result

Next, you multiply the result by 100. By plugging the values into the proceeding formula, you acquire the quotient between the number of values below your score and the number of all the values in your data set. Multiplying the quotient by 100 results in a percentage. If we return to the previous test score example, the process looks like the calculation below:

(10÷15) x 100 = 0.66 x 100 = 66%

The result shows that the student's score of 88 is in the 66th percentile.

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Understanding percentile rank

Percentile rank represents a type of statistical organisation. Percentile rank refers to the percentage of scores that are equal to or less than a given score. To calculate percentile rank, you begin with a closed set of values, meaning that you're working with a defined set and a finite number of values. Test scores, patient blood pressure values or employee overtime hours are usually good sets for determining percentile rank, as the values are specific and countable. Similar to percentages, percentile ranks fall on a continuum from 0 to 100.

If you took a standardised test and your score is greater than or equal to 93% of the other test-takers' scores, your percentile rank is in the 93rd percentile. Remember, a percentile rank may not denote an actual exam score or other assessment scores. Percentile rank only represents a value's rank as compared to other values in a larger group that has placed between 0 and 100. The most popular formula for calculating percentile rank is:

Percentile rank = p / 100 x (n + 1)

In the equation given, p represents the percentile and n represents the total number of items in the data set.

How to find percentile rank

With the percentile value in hand, you may proceed with determining percentile rank. This may be preferable to calculating a percentage for some, as having a ranking may be easier to interpret in the given context. The steps below illustrate how to apply the formula in the previous section for calculating percentile rank.

1. Calculate the percentile of your data set

You may begin by calculating the percentile of the data set you are measuring first unless you already have this data at hand.

Example: You are trying to calculate the percentile rank of a test score, this time in the 80th percentile. The value 80 represents the percentile in this case, which you may use in the formula to find percentile rank. Substitute 80 for the variable p in the formula:

Percentile rank = 80 / [100 x (n + 1)]

2. Find the number of items in the data set

The n variable represents the total number of values in your data set and is something you discover before finding the percentile rank. In many cases, you might simply count up the number of items you're working with.

Example: You're working with 25 test scores, so variable n equals 25. As you insert the value 25 into the formula below, remember to add the number 1 to n, resulting in a formula that looks like this:

Percentile rank = 80 / [100 x (25 + 1)]

Which becomes:

Percentile rank = 80 / (100 x 26)

3. Multiply the sum by 100

Once you've added 1 to your n value, you proceed by multiplying the sum by 100.

Example: Here, you multiply 26 by 100:

Percentile rank = 80 / (100 x 26) = 80 / 2,600

Your result is 2600.

4. Divide the percentile

You calculate the percentile rank in the final step. You divide the figure you got in the last step by the percentile value you found in the first step.

Example: You divide 80 by 2600. The final value is 0.03 or the 3rd percentile rank. The calculations appear as follows:

Percentile rank = 80 / 2,600 = 0.03 = 3rd percentile rank

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How to calculate percentile range

Percentile range represents another important value in the world of statistics. Percentile range refers to the difference between two different percentiles. For instance, a social scientist measuring survey data might calculate the percentile range between two types of demographics to compare various types of information. Typically, statisticians calculate the percentile range between the 10th and 90th percentiles, but they might calculate the range between any two percentiles. Below, is the formula to discover the percentile range between the 10th and 90th for a given value:

(90th percentile) - (10th percentile)

Here are the steps to follow:

1. Find the percentile ranks of your values

If you know the percentile rank of two values, you're able to calculate the percentile range.

Example: Assume you are measuring the weight of 10 tigers at various stages of life. If one tiger's weight of 10 pounds is at the 10th percentile and another's weight of 120 pounds is at the 90th percentile, you find the difference through simple subtraction. You subtract the value in the 10th percentile rank from the value in the 90th percentile rank:

Percentile range = (90th percentile) - (10th percentile) = 120 - 10 = 110

2. Interpret your results

The percentile range simply compares two different percentile ranking items. You usually get a better idea of the characteristics of your data by finding the percentile range.

Example: When measuring the weight of different tigers, the percentile range of 110 means that 110 other possible weights might be above or below the average.

Business professionals, field scientists and social scientists often find percentile ranges useful when assessing large data sets and trying to find relevant patterns.

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