Question

Find The following percentiles using this data: 40,45,50,50,56,60,65,80,90

1. 75th percentile

a. 65

b. 56

c. 50

d. 90

2. 95th percentile

a. 65

b. 56

c. 80

d. 90

Answer 1

$$40,45,50,50,56,60,65,80,90$$

$n = 9$

1.

$$i=\dfrac{75}{100}(9)=6.75$$

Since the index $i$ is not an integer, round up: $i = 7.$

The percentile is at the position $i = 7.$

So, the percentile is $65.$

a. 65

2.

$$i=\dfrac{95}{100}(9)=8.55$$

Since the index $i$ is not an integer, round up: $i = 9.$

The percentile is at the position $i = 9.$

So, the percentile is $90.$

d. 90