Question

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. compute the 20th, 25th, 65th, and 75th percentiles. if needed, round your answers to two decimal digits.

Answer 1

The 20th percentile is 20,

The 25th percentile is 22.50.

The 65th percentile is 28.

The 75th percentile is 29.

Given values:

27, 25, 20, 15, 30, 34, 28, and 25.

n = 8

sorting the data gives:

15, 20, 25, 25, 27, 28, 30, and 34.

How to solve for 20th percentile

= 20/100 * 8

= 1.6 ≈ 2

1.6 is rounded to 2, the second value is in the sorted data set is 20 hence the 20th percentile is 20

How to solve for 25th percentile

= 25/100 * 8

= 2

Since 2 is an integer, the mean of the 2nd and the 3rd values in the sorted data set gives the 25th percentile.

( 20 + 25 ) / 2 = 22.5

hence the 25th percentile is 22.50

How to solve for 65th percentile

= 65/100 * 8

= 5.2 ≈ 6

5.6 is rounded to 6, the sixth value is in the sorted data set is 28 hence the 65th percentile is 28

How to solve for 75th percentile

= 75/100 * 8

= 6

Since 6 is an integer, the mean of the 6th and the 7th values in the sorted data set gives the 75th percentile.

( 28 + 30 ) / 2 = 29

hence the 75th percentile is 29

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