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 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.

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

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 10^th 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 10^th rank. Hence x will be 10.
Identifying the count of same 10^th 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.

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 as 50^th 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 4^nd 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 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 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!!