Everything Maths Grade 11

CHAPTER 18. STATISTICS 18.3

minimum

data value

maximum

data value

first

quartile

third

quartile

median

Data Values

-4 -2 0 2 4

Figure 18.2: Main features of a box and whiskerdiagram

Example 2: Box and Whisker Diagram

QUESTION

Draw a box and whisker diagram for the data set

x ={ 1 ,25; 1,5; 2,5; 2,5; 3,1; 3,2; 4,1; 4,25; 4,75; 4,8; 4,95; 5, 1 }.

SOLUTION

Step 1 : Determine the five number summary

Minimum = 1 , 25

Maximum = 5 , 10

Position of first quartile= between 3 and 4

Position of second quartile = between 6 and 7

Position of third quartile= between 9 and 10

Data value between 3 and 4 =^12 (2,5 + 2,5) = 2, 5

Data value between 6 and 7 =^12 (3,2 + 4,1) = 3, 65

Data value between 9 and 10 =^12 (4,75 + 4,8) = 4, 775

The five number summary is therefore: 1 ,25; 2,5; 3,65; 4,775; 5, 10.

Step 2 : Draw a box and whisker diagram and markthe positions of the minimum,

maximum and quartiles.

minimum maximum

first

quartile

third

quartile

median

Data Values

1 2 3 4 5