Before we understand the percentile rank, let’s understand “Percentile” first. I won’t go through the details of percentile like P50= median and all, I’ll try to keep it simple.
Meaning of Percentile
The percentiles divide the observations of the data arranged in increasing order of their magnitudes into 100 equal parts and they are denoted by symbols P1, P2, P3….P99.
Why Percentile Rank?
If we know the marks or rank of the students in the context of the marks secured by the entire class, then we can correctly evaluate the level of his or her cleverness. This can essentially be done by finding the percentile rank of the student.
It is well-known that ranks are given to the observations of un-grouped data arranged in increasing order of their magnitude. If three observations of data are 47, 29, and 25, then their corresponding ranks are 1,2 and 3.
A student in a group of 40 students in a subject gets the 25th rank and another student in a group of 200 students gets the 25th rank in the same subject, then it is not proper or advisable to say that the two students are equally clever because they are the same rank.
If two specified students belonging to different groups get the same ranks, then the superiority of one over the other can be determined on the base of their percentile rank.
What is Percentile Rank?
Two individuals coming from two different groups have the same rank in the subject or some activity then it is essential to convert their ranks into percentile rank in order to determine their excellence or competence in the subject or activity. The simple rank and percentile rank will be denoted by symbols R and PR respectively.
The formula of PR:
The formula for converting the simple rank into PR is..
PR =100 [1- (R-0.5/n)]
Where, PR = Percentile Rank, R= Simple Rank, n= Number of individual or items in a group.
Percentile Rank illustration:
Let's make it more clear, by taking the below illustration.
Question: The rank of a student out of 50 students of different schools in an Essay Competition is 5. Find the PR of the student and interpret it.
Answer : PR =100 [1- (R-0.5/n)] Where, R= 5 and n=50
= 100 [ 1- (5 - 0.5/50]
= 100 [1 - (4.5/50)]
=100 [ 1 - 0.09 ]
=100 [0.91]
PR=91
Interpretation:
PR 91 means that the student with 5th rank is superior to 91% of the students in the group.
Now keeping the above example in mind you can easily understand the meaning when a person says that he or she scored 95 percentile in the exam. It simply means that person’s rank is superior to 95% of the students in the group.
In other words, Percentile ranking is the ranking of any item based on its performance as compared to others in the same category.
Percentile rankings are percentages and are used in many fields, such as academic exams, marketing, and sales. There are many ways to get percentile rankings, but the most common method is called the .67 method.
Percentile ranking is a method of ordering the data in an experiment. It indicates the percentage of data in the experiment that is equal to the given value.
For example, if the value of 1st percentile is 0, 50th percentile is the median, and the value of the 99th percentile is 6, then there are 6 data points in the experiment that have value equal to 6 and rest of the values have values less than 6.
Percentile rank is a measure that tells you where your score falls in the distribution of scores in a data set.
So, a score of X in a test with a score scale of Y is ranked in a percentile of Z (eg. 80th % means that your score of 80 falls in the 80th place in the distribution of scores).
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