Question

The table below shows the number of citizens in four towns with heights in various ranges. The heights of the citizens in which town represent an extreme distribution? Town A Town B Town C Town D Taller than 5' 3'' but shorter than 5' 6'' 21 13 25 23 Taller than 5' 6'' but shorter than 5' 9'' 39 56 33 32 Taller than 5' 9'' but shorter than 6' 0'' 45 78 39 54 Taller than 6' 0'' but shorter than 6' 3'' 32 49 48 46 Taller than 6' 3'' but shorter than 6' 6'' 16 19 60 31

Answer 1

The answer is (Town B)

Answer 2

First we form the table from the data given as shown below:

Town A B C D

Taller than 5'3" but shorter than 5'6" 21 13 25 33

Taller than 5'6" but shorter than 5'9" 39 56 33 32

Taller than 5'9" but shorter than 6'0" 45 78 39 54

Taller than 6'0" but shorter than 6'3" 32 49 48 46

Taller than 6'3" but shorter than 6'6" 16 19 60 31

Next, we identify the minimum and the maximum to calculate the range as shown in the table below:

The range is defined as the maximum - minimum

Town A B C D

Taller than 5'3" but shorter than 5'6" 21 13 25 33

Taller than 5'6" but shorter than 5'9" 39 56 33 32

Taller than 5'9" but shorter than 6'0" 45 78 39 54

Taller than 6'0" but shorter than 6'3" 32 49 48 46

Taller than 6'3" but shorter than 6'6" 16 19 60 31

Minimum Value 16 13 25 31

Maximum Value 45 78 69 54

Range 29 65 44 23

As we can see the range is highest for town B (which is 65)

Hence Town B represents an extreme distribution