Question

Consider a sample with data values of 27, 24, 21, 16, 30, 35, 28, and 24. Compute the 20th, 25th, 65th, and 75th percentiles. 20th percentile 1 1.8 Incorrect: Your answer is incorrect. 25th percentile 2 2.25 Incorrect: Your answer is incorrect. 65th percentile 3 5.85 Incorrect: Your answer is incorrect. 75th percentile

Answer 1

20

21.75

27.85

29.5

Explanation:

Arranging the values in ascending order we get

16 21 24 24 27 28 30 35

n = Number of values = 8

Rank is given by

`\frac{\text{Percentile}}{100}* (n+1)`

`=(20)/(100)(8+1)=1.8`

Taking the fraction of the rank i.e., 0.8 and work out the weighted mean

`0.8* (21-16)+16=20`

The 20th percentile is 20

`(25)/(100)(8+1)=2.25`

`0.25(24-21)+21=21.75`

The 25th percentile is 21.75

`(65)/(100)(8+1)=5.85`

`0.85(28-27)+27=27.85`

The 65th percentile is 27.85

`(75)/(100)(8+1)=6.75`

`0.75(30-28)+28=29.5`

The 75th percentile is 29.5