Decile for grouped data can be calculated from the following formulae;
Where, ℓ= 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).
ℓ= 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.
