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

Answer:

20

21.75

27.85

29.5

Step-by-step 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

$\dfrac{\text{Percentile}}{100}\times (n+1)$

$=\dfrac{20}{100}(8+1)=1.8$

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

$0.8\times (21-16)+16=20$

The 20th percentile is 20

$\dfrac{25}{100}(8+1)=2.25$

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

The 25th percentile is 21.75

$\dfrac{65}{100}(8+1)=5.85$

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

The 65th percentile is 27.85

$\dfrac{75}{100}(8+1)=6.75$

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

The 75th percentile is 29.5