Question

Consider a sample with data values of 26, 25, 22, 16, 32, 33, 29, and 25. Compute the 20th, 25th, 65th, and 75th percentiles (to 1 decimal, if decimals are necessary).

Answer 1

Solution:

Given that,

16, 22, 25, 25, 26, 29, 32, 33

n = 8

The 20th pecentile = ( P / 100 * n )

= ( 20 / 100 * 8 )

= ( 0.2 * 8)

= 1.6

= 2

The percentile is at the position = 2 it is 22

The 20th pecentile is 22

The 25th pecentile = ( P / 100 * n )

= ( 25 / 100 * 8 )

= ( 0.25 * 8)

= 2.0

The percentile is at the position = 2 it is 22 and at postion + 1 = 3 is 25

Their average is the percentile = ( 22 +25 / 2)

= 47 /2

= 23.5

The 25th pecentile is 23.5

The 65th pecentile = ( P / 100 * n )

= ( 65 / 100 * 8 )

= ( 0.2 * 8)

= 5.2

= 6

The percentile is at the position = 6 it is 29

The 65th pecentile is 29

The 75th pecentile = ( P / 100 * n )

= ( 75 / 100 * 8 )

= ( 0.75 * 8)

= 6.0

The percentile is at the position = 6 it is 29 and at postion + 1 = 7 is 35

Their average is the percentile = ( 29 +32 / 2)

= 61 /2

= 30.5

The 75th pecentile is 30.5