The arranged data can be divided into ten equal parts by nine values. These values are called deciles and denoted by D1, D2,…….D9. Two different types of formulas are used for the calculation of deciles in case of grouped data (data presented in frequency distribution) and ungrouped data (data in original form). The calculation of deciles for both grouped and ungrouped data is explained below with the help of simple problems.

Calculation of Deciles for Ungrouped Data

Deciles of ungrouped data can be calculated with the help of following formula:

Problem: The twelve donors donated the following amount in a charity fund: 500, 850, 925, 800, 600, 750, 650, 625, 800, 400, 725, and 550. Find D4, D7 and D9

Arrange data in ascending order:
400, 500, 550, 600, 625, 650, 725, 750, 800, 800, 850, 925

Fourth Decile (D4)

D4 can be calculated by using the formula:

Since 5.2th observations lies between 5th and 6th value in the ordered group, or midway between 625 and 650 therefore

Seventh Decile (D7)

The calculation of seventh decile is given as:

Ninth Decile (D9)

The calculation of D9 is given below:

Calculation of Deciles for Frequency Distribution

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

Problem: The daily earnings of employees working at an industrial complex are given below in table. Find D2, D5 and D9.

Solution:

2nd Decile (D2)

In case of frequency distribution 2nd decile can be calculated by using the formula given below:

5th Decile

The calculation of 5th decile is given below:

9th Decile

The calculation of 9th decile is shown in the figure below: