Answer:
20th percentile = 19
25th percentile = 21.5
65th percentile = 28
75th percentile = 30
Step by Step Explanation:
Computation for the 20th, 25th, 65th, and 75th percentiles
First step is to arrange sample with data values of 27, 24, 19, 14, 30, 35, 28, and 24 in Ascending order
Ascending order of given data
14,19,24,24,27,28,30,35
Now let Compute for the 20th, 25th, 65th, and 75th percentiles
Using this formula
I=P/100*n
Where,
n =8 given data values
Let plug in the formula
1. 20th PERCENTILE
20th PERCENTILE = (20/100) * 8
20th PERCENTILE= 1.6
20th PERCENTILE = 2 (rounded up to the nearest integer)
The 20th percentile is the 2th value in the given date that was arranged in ascending order which is 19
Therefore the 20th percentile is 19.
2. 25th PERCENTILE
25th PERCENTILE = (25/100) * 8
25th PERCENTILE= 2
To get the 25th percentile of 2 we would take the average of 2nd and 3rd value
25th PERCENTILE = (19 + 24)/2
25th PERCENTILE=43/2
25th PERCENTILE= 21.5
Therefore the 25th percentile is 21.5
3. 65th PERCENTILE
65th PERCENTILE = (65/100) * 8
65th PERCENTILE= 5.2
65th PERCENTILE= 6 (rounded up to the nearest integer)
The 65th PERCENTILE is the 6th value which is 28
Therefore 65th percentile is 28
4. 75th PERCENTILE
75th PERCENTILE = (75/100) * 8
75th PERCENTILE = 6
To get the 75th PERCENTILE of 6 we would take the average of 6th and 7th value
75th PERCENTILE = (28+30) / 2
75th PERCENTILE =58/2
75th PERCENTILE = 29
Therefore the 75th percentile is 30
Therefore the 20th, 25th, 65th, and 75th percentiles are:
20th percentile = 19
25th percentile = 21.5
65th percentile = 28
75th percentile = 30
