Percentile Rank Formula

Percentile rank formula is used to give rank percentile of a given list, in normal calculations we know the formula is R = p/100(n+1), in excel we use the rank.eq function with the count function to calculate the rank percentile of a given list.

Formula to Calculate Percentile Rank

Percentile Rank is the percentage of scores that shall be equal to, or it could be less than a given value or given score. Percentile like percentage also falls within the range of 0 to 100. Mathematically, it is represented as,

R = P / 100 (N + 1)
Percentile Rank Formula

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For eg:
Source: Percentile Rank Formula (wallstreetmojo.com)

Where,

  • R is Percentile Rank,
  • P is Percentile,
  • N is the Number of Items.

Explanation

The formula which is being discussed here depicts how many of the scores, or the observations fall behind a particular rank. For example, one observation gets 90 percentile; it does not mean that the observation score is 90% out of 100, but rather it states that the observation has performed at-least what other 90% observations are or is above those observations. Hence, the formula incorporates the number of observations in it and multiples it with the percentile, and provides the position where that observation would lie. So, after the data is arranged from lowest to largest and rank is provided to each observation, then only we can use the number derived from the formula and conclude that observation lies at the asked percentile.

Examples

You can download this Percentile Rank Formula Excel Template here – Percentile Rank Formula Excel Template

Example #1

Consider a data set of following numbers: 122, 112, 114, 17, 118, 116, 111, 115, 112. You are required to calculate 25th Percentile Rank.

Solution:

Use the following data for the calculation of percentile rank.

Percentile Rank Formula Example 1

So, The Calculation of Rank can be done as follows-

Example 1.1

R = P/100(N+1)

= 25/100(9+1)

Rank will be –

 Example 1.2

Rank = 2.5th rank.

Percentile Rank will be –

 Example 1.3

Since the rank is an odd number, we can take an average of 2nd term and 3rd term, which is (111 + 112)/ 2 = 111.50

Example #2

William, a well-known animal doctor, is currently working on the health of elephants and is in the process of creating medication to treat elephants from a common disease they suffer from. But for that, he first wants to know the average percentage of elephants that fall below 1185.

  • For that, he has collected a sample of 10 elephants, and their weight in kgs is as follows:
  • 1155, 1169, 1188, 1150, 1177, 1145, 1140, 1190, 1175, 1156.
  • Use the Percentile Rank formula to find the 75th Percentile.

Solution:

Use the following data for the calculation of percentile rank.

Percentile Rank Formula Example 2

So, The Calculation of Rank can be done as follows-

Example 2.1

R= P / 100 (N + 1)

=75 / 100 (10 + 1)

Rank will be –

Example 2.2

Rank= 8.25 rank.

Percentile Rank will be –

8th term is 1177 and now adding to this 0.25 * (1188 – 1177) which is 2.75, and the result is 1179.75

Percentile Rank = 1179.75

Example #3

IIM institute wants to declare their result out for each student in relative terms, and they have come out with the idea of instead of providing percentages, they want to provide a relative ranking. The data is for the 25 students. Using the Percentile Rank formula, find out what will be the 96th percentile rank?

Solution:

The number of observations here is 25, and our first step would be arranging data Rank-wise.Percentile Rank Formula Example 3

So, The Calculation of Rank can be done as follows-

Example 3.1

R= P/100(N+1)

= 96/100(25+1)

= 0.96*26

Rank will be –

 Example 3.2

Rank =24.96 rank

Percentile Rank will be –

24th term is 488 and now adding to this 0.96 * (489 – 488) which is 0.96, and the result is 488.96

Example #4

Let us now determine the value through the excel template for Practical example I.

Solution:

Use the following data for the calculation of percentile rank.

Percentile Rank Formula Example 4

So, The Calculation of Percentile Rank can be done as follows-

Example 4.1

Percentile Rank will be –

Example 4.2

Percentile Rank = 1179.75

Relevance and Use of Percentile Rank Formula

Percentile ranks are much useful when someone wants to understand quickly as to how a particular score will compare to the other values or observations or scores in a given dataset or in a given distribution of scores. Percentiles are mostly used in the field of statistics and in the field of education, where instead of providing relevant percentages to the students, they instead give them relative rankings. And if one is interested in the relative ranking, then mean, actual values, or the variance, which is the standard deviation, will not be useful. So, it can be concluded that percentile rank gives you the picture relative to other always not an absolute value or absolute answer that is in relation to other observations and not in relation to mean. Further, some financial analyst uses this criterion to screen the stocks where they could be using any of the financial key metrics and picking the stock, which lies in the 90th percentile.

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