Percentile Formula

Percentile calculation is in everyday use. Mostly we can define percentile as a number where a certain percentage of scores fall below that given number. We might know that when someone scored 65 out of 90 on a test. But this figure has no real meaning unless we know what percentile he falls into. If we know that score is in the 90th percentile, then it means this score is better than 90% of the people who took the test. In this article, the student will learn about the percentile formula and its concepts with the examples. Let us learn it!

What is Percentile?

In mathematics, we use this term percentile informally to indicate that a certain percentage falls below that percentile value. For example, if we score in the 25th percentile, then 25% of test-takers are below this your score. Here 25 is called the percentile rank. In the statistical, it can get a little more complicated.

Percentile divides a data set into the 100 equal parts. A percentile is a measurement that tells us what percent of the total frequency of a data set was at or below that measure. As an example, let us consider a student’s percentile in some exams.

If on this test, a given student scored in the 60th percentile on the quantitative section, she scored at or better than 60% of the other students. Further, if a total of 500 students took the test, then this student scored at or better than \(500 \times 0.60 = 300\) students out of 500 students. In other words, 200 students scored better than that particular student.

Source: en.wikipedia.org

Therefore, percentiles are used to understand and interpret the given data. They also indicate the values below which a certain percentage of the data in a data set is found. Percentiles are frequently useful to understand the test scores and biometric measurements in our day-to-day routine.

Formula for Percentile

\(Percentile = \frac{Number \ of \ Values \ Below \ some \ value \ “x”} {Total \ Number\  of \ Values} \times  100\)

OR

\(P =\frac{n}{N} \times 100\)

N	Number of values in the data set
n	The ordinal rank of a given values
P	Percentile

Solved Examples for Percentile Formula

Q.1: The scores for some candidates in a test are 40, 45, 49, 53, 61, 65, 71, 79, 85, 91. What will be the percentile for the score 71? Use the percentile formula.

Solution: Given parameters:

No. of. Scores below the value “71” i.e. n = 6

Total no. of. Scores i.e. N = 10

The formula for percentile is given as below:

\(P =\frac{n}{N} \times 100\\\)

\(P = \frac{6}{10} \times 100\\ = 60\)

Thus, Percentile of 71 will be 60.

Q.2: The scores for some candidates in a test are 40, 45, 49, 53, 61, 65, 71, 79, 85, 91. What will be the score with a percentile value of 90?

Solution:  It is obvious that we need to find the score “x” with percentile 90 for the given data set.

Thus, No. of. Scores below the value “x” i.e. n =?

Total no. of. Scores i.e. N = 10

Given percentile value, P = 90

The formula for percentile is given as below:

\(P =\frac{n}{N} \times 100\)

Rearranging this formula we get:

\(n = \frac {P \times N}{100}\)

\(n = \frac {90 \times 10}{100} = 9\)

Thus 9th value in the data set i.e. 85 will be the score with 90 percentile.