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 common term in statistics that is derived from Percentile. Percentile (also known as centile) is the percentage of scores ranging from 0 to 100 that are less than or equal to the given set of distributions. 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 the percentile.

A formula for Percentile Rank is given by:

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

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).

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 25^th percentile is known as one quartile. Out of 100, the 25^th percentile is known as the 1^st quartile. The 50^th percentile is known as the 2^nd quartile or median, and the 75^th percentile is known as the 3^rd quartile. The difference between the 3^rd and 1^st 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.

Example #1

Assume that a class has 20 students. All are taking the NEET exam to further their education. Babu and Sudha are two of the 20 students, and both are ranked 10th. Calculate Babu’s Percentile Rank.

Solution:

• The 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 10^th rank. Hence x will be 10.
• We need to identify the count of the same 10^th rank. In this case, it will be Babu and Sudha. So R will be 2.
• We need to count the ranks that are less than 10, which will be considered as M. Hence M will be 9.

Percentile Rank is calculated using the formula given below

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

• 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 at the 50^th percentile in his class!!

Example #2

There are 10 students who attended the 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

• The 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 4th rank. Hence x will be 4.
• Count the ranks at 4 which will be considered as “M”. Hence M will be 4.
• We need to identify the count of the same 10^th rank. In this case, it will be 0. So we will be using the second formula.

Percentile Rank is calculated using the formula given below

Percentile Rank = [M / Y] x 100

• 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 the Percentile Rank value.

Step 1: Note down the value of the 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 it is the same score as x. If yes, 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

Percentile Rank Formula in Excel (With Excel Template)

Here we will see an 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

Percentile Rank is calculated using the formula given below

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

• 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

Percentile Rank is calculated using the formula given below

Percentile Rank = [M / Y] x 100

• 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 have discussed how to calculate Percentile Rank along with practical examples. We have also provided a Percentile Rank calculator with a downloadable excel template. You may also look at the following articles to learn more –

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