The data arranged in ascending or descending order can be divided into 100 equal parts by 99 values. These values are called percentiles and denoted by P1, P2,………..P99. There is a slight difference in the calculation of percentiles in case of grouped and ungrouped data. Therefore calculation for both types of data is explained with the help of problems.
Calculation of Percentiles for Ungrouped Data
Percentiles of ungrouped data can be calculated with the help of following formula:
Problem: The data given below shows the marks obtained by the MBA students in statistics 36, 28, 47, 40, 44, 44, 39, 33, 33, 32, 48, 34, 38, 27, 40, 37, 41, 42, 38, 48, 43, 35, 37, 37, 25
Solution
Arrange data in ascending order:
25, 27, 28, 32, 33, 33, 34, 35, 36, 37, 37, 37, 38, 38, 39, 40, 40, 41, 42, 43, 44, 44, 47, 48, 48
25th Percentile (P25)
P25 can be calculated by using the formula:
50th Percentile (P50)
The calculation of P50 is given below:
Since the value of 13th observation in arranged data is 38.00 therefore P50 is also 38.
75th Percentile (P75)
The formula for calculating P75 is given below:
Calculation of Percentiles for Frequency Distribution
In case of frequency distribution, percentiles can be calculated by using the formula:
it is very good in explaining about this topic,..and i easily learn oiut of it
Thank you, the topic has helped me alot
How to find percentile using % ?
How about finding of p1 for any given data between number 1-98
Nice write up.It is really self-explanatory.
How about finding P98? Using the formula, we will be able to solve that P98 is the 25.48th item. However, we only have 25 items. How do we compute or explain it? Because we already went beyond the value of n.