# A Quick Guide on How to Calculate Percentiles

Most of the competitive entrance exams declare the results of the applicants based on percentiles. This article will tell you about how to calculate percentiles and what exactly are they?

ScienceStruck Staff

Last Updated: Jun 3, 2018

*Per cent*' is a Latin term which means '

*per hundred*'. We have already discussed what a percentage is, but what exactly is a percentile? A percentile, also known as a

*centile*, is a number or measure that expresses the number of frequencies that are below that particular measure. I am not surprised if you are confused, but here is an example that will clear the confusion. Suppose you scored 99 percentile in an exam and there are about 100 people who gave that exam. Here, 100 are the total number of frequencies or observations.

*A percentile expresses the number of frequencies that are below your measure.*If your measure is 99, it means that there are 98 students that you have outnumbered in the exam. Did you understand the difference between a percentage and percentile? If you have scored 99 percentile, it doesn't mean that you have scored 99 percent, it means that you have outnumbered 98 others who are below you, and only one student ahead of you. Keep reading to understand more on how to calculate percentiles and help yourself understand the concept in a better way.

How to go About Calculating Percentiles?

Formula to Calculate Percentiles

As mentioned earlier, there are various different approaches to calculate a percentile. This approach is the simplest one which will give you the basic idea of how you need to calculate your percentile rank or your percentile score.

Let us take an example so that you understand which value refers to which variable in the above formula. Say for instance, we have a set of values or observations and we need to calculate the percentiles of the given observations. These values are:

Now if I ask you to look at the aforementioned table and tell me which is the 50th percentile, what would you answer? Yes, 50 is the percentile of the measurement (

Here, we have pi = 20 and n = 5, so the expression can be represented as follows,

So, this expression gives that the 20th percentile (what we started with) corresponds to x = 1.5, which we calculated.

**pi = 100 (i - 0.5) / n**Let us take an example so that you understand which value refers to which variable in the above formula. Say for instance, we have a set of values or observations and we need to calculate the percentiles of the given observations. These values are:

1 | 3 | 5 | 7 | 9 |

*i*would be the sorted order of this data. So, in this case the value of*i*would be,x_{i} |
1 | 3 | 5 | 7 | 9 |

i |
1 | 2 | 3 | 4 | 5 |

*n*is the total number of values or observations given to you, which in this case is 5. So, now if we need to calculate the percentiles, the approach to the same would be,*p*._{i}= 100 (i - 0.5) / n- p
_{1}= 100 (1 - 0.5) / 5 = 10 - p
_{2}= 100 (2 - 0.5) / 5 = 30 - p
_{3}= 100 (3 - 0.5) / 5 = 50 - p
_{4}= 100 (4 - 0.5) / 5 = 70 - p
_{5}= 100 (5 - 0.5) / 5 = 90

**, we have***x*_{i}**and we have the***i***.***p*_{i}x_{i} |
1 | 3 | 5 | 7 | 9 |

i |
1 | 2 | 3 | 4 | 5 |

p_{i} |
10 | 30 | 50 | 70 | 90 |

Now if I ask you to look at the aforementioned table and tell me which is the 50th percentile, what would you answer? Yes, 50 is the percentile of the measurement (

*x*) 5. So, the 50th percentile is 5. Similarly, if you need to calculate the 20th percentile, then applying the formula, the calculation would be something like,*pi = 100 (i - 0.5) / n*Here, we have pi = 20 and n = 5, so the expression can be represented as follows,

*20 = 100 (x - 0.5) / 5 = 1.5*So, this expression gives that the 20th percentile (what we started with) corresponds to x = 1.5, which we calculated.