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**Formula for Percentile Rank (Table of Contents)**

## What is the Percentile Rank Formula?

Percentile Rank is the percentage of scores which 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, Percentile Rank Formula is represented as,

**R = P / 100 (N + 1)**

Where,

- R is Percentile Rank,
- P is Percentile,
- N is The Number of Items.

### Explanation of the Percentile Rank Formula

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 means that 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 than those observations. Hence, the formula incorporates the number of observations in it and multiples it with the percentile and provide 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 formula and conclude that observation lies at the asked percentile.

### Percentile Rank Formula Examples (with Excel Template)

Let’s see some simple to advanced examples of percentile rank formula to understand it better.

#### Example #1

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

**Solution:**

Use the following data for the calculation of percentile rank.

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

4.9 (1,353 ratings)

Using this Percentile Rank formula ,

R = P / 100 (N + 1)

= 25 / 100 (9 + 1)

Rank will be –

Rank = 2.5^{th} rank.

Percentile Rank will be –

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

**Percentile Rank =111.50**

#### Example #2

**William a well-known animal doctor is currently working upon 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 falls below 1185.**

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

**Solution:**

Use the following data for the calculation of percentile rank.

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

R= P / 100 (N + 1)

=75 / 100 (10 + 1)

Rank will be –

Rank= 8.25 rank.

Percentile Rank will be –

8^{th} 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 96 ^{th} percentile rank?**

**Solution:**

The number of observations here is 25 and our first step would be arranging data Rank-wise.

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

Using this Percentile Rank formula,

R= P / 100 (N + 1)

= 96 / 100 (25+1)

= 0.96*26

Rank will be –

Rank =24.96 rank

Percentile Rank will be –

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

**Percentile Rank = 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.

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

Percentile Rank will be –

**Percentile Rank = 1179.75**

### Relevance and Use

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 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 90^{th} percentile.

### Recommended Articles

This has been a guide to Percentile Rank Formula. Here we discuss how to calculate percentile rank in excel with practical examples and downloadable excel template. You can learn more about excel modeling from the following articles –

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