Question

The weights (in pounds) of 18 preschool children are

32, 20, 25, 27, 31, 22, 30, 23, 44, 37, 33, 45, 41, 24, 34, 21, 39, 29

Answer 1

22.8 and 37.5

Answer 2

22.8 and 37.5

Explanation:

Given the

The weights (in pounds) of 18 preschool children are

32, 20, 25, 27, 31, 22, 30, 23, 44, 37, 33, 45, 41, 24, 34, 21, 39, 29

To find its 20th percentile and 75th percentile.

In ascending order we get like this

Position X (Asc. Order)

1 20

2 21

3 22

4 23

5 24

6 25

7 27

8 29

9 30

10 31

11 32

12 33

13 34

14 37

15 39

16 41

17 44

18 45

Percentile position = (no of entries +1)20/100 = 19/5 = 3.8

Since posiiton is not integer we use interpolation method.

The value of 3.8 - 3 = 0.8 corresponds to the proportion of the distance between 22 and 23 where the percentile we are looking for is located at.

Hence 20th percentile =
`22+0.8(23-22)=22.8`

So answer is 22.8

----------------------

75th percentile

Percentile posiiton = 19(75)/100 = 14.25

75th percentile=
`37+0.25(39-37)=37.5`