Percentile – Calculating Percentile

This is widely used in calculating the positions of students participated in entrance exams, though the calculations vary slightly.

The pth percentile of a data set is a value such that at least p % of the items in
the dataset have a value equal to or less than the value of the data item. It also means that
(100 - p) % of the items have a value more than the value of the data item.

Calculating Percentile
Percentile can be calculated using the following approach:

Arrange the data in ascending order.
The position of the pth  percentile item, i = (p/100) * n where n is the total numbers in the data sample.
If i is not an integer, round up. The pth percentile is the value in the ith position.
If i is an integer, the pth percentile is the average of the values in positions ‘i’ and ‘i +1’.
 
Calculating 90th Percentile

Consider the below sample of data.

5,6,2,3,4,4,4,5,8,9 

Arrange the data in ascending order

2,3,4,4,4,5,5,6,8,9

i = (p/100) * n = (90/100) x 10 = 9

Averaging the 9th and 10th data value you get 90th percentile = (8 +9)/2 = 8.5

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March 14, 2010 | Filed Under Basic Mathematics 

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