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

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

TownABC D

Taller than 5'3" but shorter than 5'6"21132533

Taller than 5'6" but shorter than 5'9"39563332

Taller than 5'9" but shorter than 6'0"45783954

Taller than 6'0" but shorter than 6'3"32494846

Taller than 6'3" but shorter than 6'6"16196031

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

TownABC D

Taller than 5'3" but shorter than 5'6"21132533

Taller than 5'6" but shorter than 5'9"39563332

Taller than 5'9" but shorter than 6'0"45783954

Taller than 6'0" but shorter than 6'3"32494846

Taller than 6'3" but shorter than 6'6"16196031

Minimum Value16132531

Maximum Value45786954

Range29654423

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

Hence Town B represents an extreme distribution