Question

Consider a sample with data values of 27, 24, 22, 16, 30, 35, 29, and 24. Compute the 20th, 25th, 65th, and 75th percentiles (to 1 decimal, if decimals are necessary).

Answer 1

ANSWER:

Given that,

Consider a sample with data values of 27, 24, 22, 16, 30, 35, 29, and 24. Compute the 20th, 25th, 65th, and 75th percentiles (to 1 decimal, if decimals are necessary).

Sort the data value from smallest to largest:

16

22

24

24

27

29

30

35

Let n = number of values in the data set = 8

The x^th percentile is the ((x/100)*n) th in the sorted data set,

Similarly,

20th percentile = (x/100)*n = (20/100) * 8 = 1.6 2 => 22

25th percentile = (x/100)*n = (25/100) * 8 = 2 => (22+24)/2 = 23

65th percentile = (x/100)*n = (65/100) * 8 = 5.2 6 => 29

75th percentile = (x/100)*n = (75/100) * 8 = 6 => (29+30)/2 = 29.5

The required answer is,

22 , 23 , 29 , 29.5

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