Calculation of Deciles for Grouped Data

Decile for Grouped Data

Decile for grouped data can be calculated from the following formulae;

Where,
= lower boundary of the class containing the D2 or D9, i.e. the class corresponding to the cumulative frequency in which 2N/10 or 9N/10 lies
w= class interval size of the class containing D2 or D9
f= frequency of the class containing D2 or D9
N= number of values, or the total frequency
C= cumulative frequency of the class preceding the class containing D2 or D9
For Example:
We will calculate fourth, seventh and ninth deciles from the frequency distribution of weights of 120 students, as provided in this table.

=182.83 pounds

Conclusion:
From D4, D7 and D9 we conclude that 40% students weigh 148.79 pounds or less, 70% students weigh 164.5 pounds or less and 90% students weigh 182.83 pounds or less.

Another example:
Find the deciles D1, D5, and D9 of the following data.

Columns Load Freqency (fi)
50-69 3
70-89 7
90-109 4
110-129 4
130-149 9

Solution:
1) Find each cumulative frequency and each real interval.


2) Remember the decile common formula of continuous or discrete distribution (Grouped Data).

= the lower boundary of relevant decile class
N= total frequency =Σf
C= the cumulative frequency of the previous interval of relevant decile class
f= the frequency of relevant decile class
w= the length of the real interval
3) Find first decile.

4) Find fifth decile.

5) Find ninth decile.

Let’s read post Calculation of Percentiles for Grouped Data.

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