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Percentile Rank Formula

By Madhuri ThakurMadhuri Thakur

Home » Finance » Blog » Finance Formula » Percentile Rank Formula

Percentile Rank Formula

Percentile Rank Formula (Table of Contents)

  • Percentile Rank Formula
  • Percentile Rank Calculator
  • Percentile Rank Formula in Excel (With Excel Template)

Percentile Rank Formula

Percentile Rank is a usual term mainly used in statistics which is arrived from Percentile. Percentile (also referred to as Centile) is the percentage of scores ranges between 0 and 100 which is less than or equal to the given set of distribution. Percentiles divide any distribution into 100 equal parts. This is predominantly used for the interpretation of scores with different ranges across various tests. Percentile Rank (PR) is arrived based on the total number of ranks and the number of ranks below and above percentile.

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A formula for Percentile Rank is given by:

To identify percentile rank (PR) of score x, out of N where x is included.

Percentile Rank = [(M + (0.5 * R)) / Y] x 100

Where,

  • M = Number of Ranks below x
  • R = Number of Ranks equals x
  • Y = Total Number of Ranks

To identify percentile rank (Per Rank) of score x, out of Y where x is not included.

Percentile Rank = [M / Y] x 100

Where,

  • M = Number of Rank at x
  • Y = Total number of Ranks

Percentile is mainly applied to the data set of scores where ranking needs to be identified. In addition, every 25th percentile is known as one quartile. Out of 100, the 25th percentile is known as 1st quartile. 50th percentile is known as 2nd quartile or median, the 75th percentile is known as 3rd quartile. The difference between 3rd and 1st quartile is called an Interquartile range.

Examples of Percentile Rank Formula

Let’s take an example to understand the calculation of Percentile Rank in a better manner.

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

Example #1

Assume there are 20 students in a class. All are attending a NEET exam for their higher studies. Babu and Sudha are two among those 20 students and both are ranking as 10th among 20. Calculate the Percentile Rank of Babu.

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Solution:

  • A total number of ranks will be the same as the total number of students in this case. So Y will be 20.
  • percentile rank needs to be calculated for Babu who is at 10th rank. Hence x will be 10.
  • Identifying the count of same 10th rank. In this case, it will be Babu and Sudha. So R will be 2.
  • Count the ranks that are less than 10 which will be considered as M. Hence M will be 9.

PRF Example 1

Percentile Rank is calculated using the formula given below

Percentile Rank = [(M + (0.5 * R)) / Y] x 100

Calculation of Percentile Rank for example 1

  • Percentile Rank = [(9 + (0.5 * 2)) / 20] * 100
  • Percentile Rank = [(9+1) / 20] * 100
  • Percentile Rank = [10 / 20] * 100
  • Percentile Rank = 0.5 * 100
  • Percentile Rank = 50%

Hence the percentile rank for Babu will be 50%. Babu standing as 50th percentile in his class!!

Example #2

There are 10 students attended Aptitude test in an organization. Scores of the students are 5, 9, 4, 12, and 7. Identify the percentile rank for score 9.

Solution:

  • Step 1: Arrange the score data set in ascending order: 4, 5, 7, 9, 12.
  • Step 2: Add ranking for the ordered score:
Score

4

5

7

9

12

Ranking

1

2

3

4

5

  • A total number of ranks will be the same as the total number of students in this case. So Y will be 5.
  • Percentile rank needs to be calculated for score 9 which is 4nd rank. Hence x will be 4.
  • Count the ranks at 4 which will be considered as “M”. Hence M will be 4.
  • Identifying the count of same 10th rank. In this case, it will be 0. So we will be using the second formula.

PF Formula 2-1

Percentile Rank is calculated using the formula given below

Percentile Rank = [M / Y] x 100

Calculation of Percentile Rank for Example 2

  • Percentile Rank = [4/5] *100
  • Percentile Rank = 0.8 * 100
  • Percentile Rank = 80%

This concludes score 9 is higher than 80% of the scores.

Explanation

Below is the step by step approach for attaining Percentile Rank value.

Step 1: Note down the value of series of scores in ascending order (lowest to highest) along with ranking in a tabular format. Count the number of scores or the last rank which will be considered as “Y – Total number of ranks”.

Step 2: Identify the score x for which the percentile needs to be calculated.

Step 3: Identify if there is the same score as x if so count the same score as “R”.

Step 4: Count the scores that are less than x which will be considered as “M”. Thus the formula is,

Percentile Rank = [(M + (0.5 * R)) / Y] x 100

Step 5: If the value of “R” is zero in step 3, then the formula is,

Percentile Rank % = [M / Y] x 100 %

Relevance and Uses

There is no universally defined formula for Percentile and Percentile Rank. However, this is predominantly used for all ranking of examinations such as NEET, GRE, SAT, LSAT, etc. This is commonly used to identify as a method to interpret the position in a standard dataset. In the current digital world, this is also used for the interpretation of medical details such as percentile laparoscopy failures during operations and also used in the field of data science as well!!

Percentile Rank Formula Calculator

You can use the following Percentile Rank Calculator

M
R
Y
Percentile Rank Formula
 

Percentile Rank Formula =
M +(0.5 * R) x 100
Y
=
0 + (0.5 * 0) x100= 0
0

Percentile Rank Formula in Excel (With Excel Template)

Here we will do the example of the Percentile Rank formula in Excel. It is very easy and simple.

In excel, there are some sets of values in Example: 1 and Example: 2 tabs. Example 1 can be used for Formula: 1 and example: 2 can be used for Formula: 2. these two are based on two different formulae as mentioned above and can be used based on the scenarios. Please follow the below steps to calculate Percentile Rank using an excel template:

For Sample A

For Sample A

Percentile Rank is calculated using the formula given below

Percentile Rank = [(M + (0.5 * R)) / Y] x 100

Result For Sample A

  • Percentile Rank = [(12 + (0.5 * 3)) / 48] * 100
  • Percentile Rank = [(12+1.5) / 48] * 100
  • Percentile Rank = [13.5 / 48] * 100
  • Percentile Rank = 0.28125 * 100
  • Percentile Rank = 28.125%

For Sample B

For Sample B

Percentile Rank is calculated using the formula given below

Percentile Rank = [M / Y] x 100

Result For Sample B

  • Percentile Rank = [4/67] *100
  • Percentile Rank = 0.05970149254 * 100
  • Percentile Rank = 5.970149254%

Recommended Articles

This has been a guide to Percentile Rank Formula. Here we discuss how to calculate Percentile Rank along with practical examples. We also provide a Percentile Rank calculator with downloadable excel template. You may also look at the following articles to learn more –

  1. How To Calculate Range Using Formula?
  2. Examples of Average Formula
  3. Formula For Relative Risk Reduction
  4. Guide To Nominal Interest Rate Formula
  5. Quartile Deviation Formula | Definition | Examples

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