Decile for grouped data can be calculated from the following formulae;
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
We will calculate fourth, seventh and ninth deciles from the frequency distribution of weights of 120 students, as provided in this table.
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.
Find the deciles D1, D5, and D9 of the following data.
|Columns Load||Freqency (fi)|
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.
4) Find fifth decile.
5) Find ninth decile.
Let’s read post Calculation of Percentiles for Grouped Data.