Deciles for Grouped Data
Deciles
Deciles are those values that divide the total frequency into 10 equal parts. The Kth decile denoted by Dk is computed as follows:
where:
LB = lower boundary of the Dk class.
N = total frequency.
cfb = cumulative frequency of the class before the the Dk class.
fdk = frequency of the Qk class.
i = size of the class interval.
k = nth quartile, where n = 1,2, 3, 4, 5, 6, 7, 8, and 9.
Example 1
Calculate the 7th decile of the Mathematics test scores of 50 students.
Solution
This means we need to find the class interval where the 35th score is contained.
Note that the 28th-38th scores belong to the class interval: 36-40.
So the 35th is also within the class interval.
The D7 class is class interval 36-40.
Therefore, the 7th decile is equivalent to the 70th percentile. Therefore, 70% of the students got a score less than or equal to 39.14.