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

Answer 1

Answer:

Percentile of 20th = 20

Percentile of 25th = 22.5

Percentile of 65th = 28

Percentile of 75th = 29

Explanation:

Sort the numbers in ascending order:

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

i = P/100 * N ( i index is the position of the number. Index 1 = 15, index 2 = 20, and so on)

Index of the 20th percentile:

20/100 * 8 = 1.6

Round 1.6 to the next integer = 2

The second number I=20

The 20th percentile is 20

Index of the 25th percentile:

25/100 * 8 = 2

Because 2 is an integer the percentile of 25th is the average of I=20 and I=25

(20+25)/2=22.5

The 25th percentile is 22.5

Index of the 65th percentile

i = 65/100 * 8 = 26.5 = 5.2

Round to the next integer = 6

The 65th percentile is 28

Index of the 75th percentile

I = 75/100 * 8 = 6

Since 6 is an integer (28+30)/2 = 29 percentile