Percentile Formula

Percentile formula is used in determining the performance of a person in comparison with others. It is used mostly in schools during results of tests to check where a person stands out from others. The percentile formula for a score ‘x’ can be defined as number of scores that fall under ‘x’ divided by total number of values in the given population. The formula is given by:

Percentile(x) = (Number of values fall under ‘x’/total number of values) × 100

P = (n/N) × 100

Where, 

P is percentile

n – Number of values below ‘x’

N – Total count of population

The above formula is used to calculate the percentile for a particular value in the population.

If we have percentile value and we need to find the ‘n’ value i.e., for which data value in population then we can rewrite the above formula as-

n = (P × N)/100

Note: First we need to sort the data/population before starting the process.

Sample Problems

Question 1: What is percentile value for the score 80 for the given population 50,100,70,80,56,60,80,75.

Solution:

The given data is not sorted. So first sort the data in ascending order.

Sorted data: 50, 56, 60, 70, 75, 80, 80, 100

Number of values fall under 80 (n) = 5

Total count of values (N) = 8

Percentile = (n/N) × 100

                = (5/8) × 100

                = 62.5

The percentile of value 80 for the given population is 62.5

Question 2: What is the percentile value for the value 60 in a given population of weights of persons 50, 55, 40, 60, 100, 95, 90, 60, 80, 75.

Solution:

The given data is not sorted. So first sort the data in ascending order.

Sorted data: 40,50,55,60,60,75,80,90,95,100

Number of values fall under 60 (n)= 3

Total count of values (N)= 10

Percentile = (n/N) x 100

                = (3/10) x 100

                = 30

The percentile of value 60 for the given population is 30

Question 3: What is the 15^th percentile for the given population of weights of persons 50, 55, 40, 60, 100, 95, 90, 60, 80, 75.

Solution:

The given data is not sorted. So first sort the data in ascending order.

Sorted data: 40,50,55,60,60,75,80,90,95,100

Given, Percentile (P)=15

Total count of values (N)= 10

Need to find n

Percentile = (n/N) x 100

From the given formula we can find n by

n= (P x N)/100

  = (15 x 10) / 100

  = 150/100

  =1.5

1.5 can be rounded off to 2

And 2^nd term in the sorted population is 50.

15^th percentile value is 50.

Question 4: What is the 50^th percentile for the given scores of 8 persons are 50, 100, 70, 80, 56, 60, 80, 75.

Solution:

The given data is not sorted. So first sort the data in ascending order.

Sorted data: 50,56,60,70,75,80,80,100

Given, Percentile (P)=50

Total count of values (N)= 8

Need to find n

Percentile = (n/N) x 100

From the given formula we can find n by

n= (P x N)/100

  = (50 x 8) / 100

  = 400/100

  =4

4^th term in the sorted population is 70.

50^th percentile value is 70.

Question 5: Find percentile for the value 6 from the given population 1, 6, 7, 3, 8, 9.

Solution:

The given data is not sorted. So first sort the data in ascending order.

Sorted data: 1,3,6,7,8,9

Number of values fall under 6 (n)= 2

Total count of values (N)= 6

Percentile = (n/N) x 100

                = (2/6) x 100

                = 100/3

                = 33.33

The percentile of value 6 for the given population is 33.33