# Percentile Formula

Percentile formula helps in determining the performance of a person in comparison to others. To recall, the percentile is used in tests and scores of a candidate to show where he/she stands with reference to other candidates. The percentile of the value â€˜xâ€™ is calculated by the ratio of the number of values below â€˜xâ€™ to the total number of values. Percentile calculation can be done for weight, income and many other things.

## Formula for Percentile

The Percentile Formula is given as,

 Percentile = (Number of Values Below “x” / Total Number of Values) Ã— 100

Also Check: Percentage Formula

Another formula to find the percentile is given by:

 P = (n/N) Ã— 100 P = (nth percentile/100)Â  Ã— Total number of values in the list

Here,Â

n = Ordinal rank of the given value or value below the number

N = Number of values in the data setÂ

P = PercentileÂ

Rank = Percentile/100

Ordinal rank for Percentile value = Rank Ã— Total number of values in the list

### Solved Example

Question 1:

The scores for student are 40, 45, 49, 53, 61, 65, 71, 79, 85, 91. What is the percentile for score 71?

Solution:

Given,

No. of. scores below 71 = 6

Total no. of. scores = 10

The formula for percentile is given as,

Percentile = (Number of Values Below “x” / Total Number of Values) Ã— 100

Percentile of 71

= (6/10) Ã— 100

= 0.6 Ã— 100 = 60

Question 2:Â

Consider the list {50, 45, 60, 25, 30}. Find the 5th, 30th, 40th, 50th and 100th percentiles of the list given.

Solution:

Given list – 50, 45, 60, 25, 30

Ordered list – 25, 30, 45, 50, 60

N = 5

 Percentile (P) Ordinal rank Percentile value 5th (5/100) Ã— 5 = [0.25] = 1 1st number in the ordered list = 25 30th (30/100) Ã— 5 = [1.5] = 2 2nd number in the ordered list = 30 40th (40/100) Ã— 5 = 2 2nd number in the ordered list = 30 50th (50/100) Ã— 5 = [2.5] = 3 3rd number in the ordered list = 45 100th (100/100) Ã— 5 = 5 5th number in the ordered list = 60