 # 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 ‘x’ is calculated by the ratio of the number of values below ‘x’ 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) × 100

Also Check: Percentage Formula

Another formula to find the percentile is given by:

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

Here,

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

N = Number of values in the data set

P = Percentile

Rank = Percentile/100

Ordinal rank for Percentile value = Rank × 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) × 100

Percentile of 71

= (6/10) × 100

= 0.6 × 100 = 60

Question 2:

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) × 5 = [0.25] = 1 1st number in the ordered list = 25 30th (30/100) × 5 = [1.5] = 2 2nd number in the ordered list = 30 40th (40/100) × 5 = 2 2nd number in the ordered list = 30 50th (50/100) × 5 = [2.5] = 3 3rd number in the ordered list = 45 100th (100/100) × 5 = 5 5th number in the ordered list = 60

#### 1 Comment

1. I feel easy to learn & teach maths . Thanks BYJUS