How to Find Percentiles in Statistics

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:

 

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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

 

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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:

 

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50th Percentile (P50)

The calculation of P50 is given below:

 

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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:

 

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Calculation of Percentiles for Frequency Distribution

In case of frequency distribution, percentiles can be calculated by using the formula:

 

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Problem: From the following frequency table of expenses incurred by employees of an organization. Calculate  P25, P40 and P75.

 

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Solution:

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25th Percentile (P25)

In case of frequency distribution 25th percentile can be calculated by using the formula given below:

 

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40th Percentile (P40)


40th percentile of frequency distribution can be calculated by using the formula given below:

 

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75th Percentile (75)

75th percentile of frequency distribution can be calculated by using the formula given below:

 

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