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11.02 Box plots

Worksheet
Box Plots
1

Consider the following box plot below and the corresponding five number summary:

Fill in the missing numbers on the box plot.

a
Minimum20
Lower Quartile28
Median36
Upper Quartile42
Maximum52
b
Minimum16
Lower Quartile33
Median47
Upper Quartile61
Maximum71
c
Minimum26
Lower Quartile33
Median41
Upper Quartile44
Maximum45
2

For each of the following box plots, construct a five number summary:

a
Scores
0
2
4
6
8
10
12
14
16
18
20
b
Scores
0
2
4
6
8
10
12
14
16
18
20
c
Scores
0
2
4
6
8
10
12
14
16
18
20
d
Scores
40
42
44
46
48
50
52
54
56
58
60
3

Create a box plot to represent the information in the following tables:

a
Minimum5
Lower Quartile25
Median40
Upper Quartile55
Maximum65
b
Minimum10
Lower quartile20
Median40
Upper quartile55
Maximum75
c
Minimum10
Lower quartile20
Median40
Upper quartile55
Maximum75
d
Minimum30
Lower quartile31
Median47
Upper quartile53
Maximum58
4

For each of the following data sets:

i

Construct the five number summary.

ii

Draw a box plot.

a

14, 15, 20, 21, 23, 24, 27

b

21, 25, 29, 31, 32, 34, 39, 40

c

40, 12, 8, 20, 12, 28, 48, 36, 60

d

28, 4, 40, 16, 20, 48, 20, 44, 56

e

42, 43, 48, 54, 59, 51, 53, 50, 57, 45

f

60, 66, 67, 68, 69, 72, 73, 76, 77, 78, 86

g
Leaf
42 3 5 8 9
50 2 3 4 6 7
61 2 4 5

Key: 1 | 2 = 12

h
Leaf
20 4 4 5 7 7
31 2 3 5 5
43 3 5 9

Key: 1 | 2 = 12

i
j
5

Consider the box plot shown:

a

State the percentage of scores that lie between each of the following values:

i

7 and 15

ii

1 and 7

iii

9 and 19

iv

7 and 19

v

1 and 15

b

In which quartile is the data the least spread out?

0
5
10
15
20
Applications
6

A geography teacher has marked a set of tests. She wants to represent the results in a box plot. She has already sorted her data and created the following table:

Create a box plot to represent the data in the table.

Minimum4
Lower Quartile10
Median22
Upper Quartile26
Maximum38
7

A mathematics teacher has marked a set of tests. She then sorted her data and created the following table:

Create a box plot to represent the data in the table.

Minimum2
Lower quartile10
Median16
Upper quartile22
Maximum30
8

The box plot shows the age at which a group of people got their driving licences:

a

What is the oldest age?

b

What is the youngest age?

c

What percentage of people were aged from 18 to 22?

d

The middle 50\% of responders were within how many years of one another?

e

In which quartile are the ages least spread out?

f

The bottom 50\% of responders were within how many years of one another?

Age
15
20
25
30
35
9

Construct a box plot for the following data set:

  • Range = 14

  • Lowest score = 2

  • IQR = 8

  • 25\% of scores are below 4

  • 50\% of scores are above 8

10

The test scores of 11 students in Science and Music are listed below:

  • Science: 52, 59, 87, 66, 74, 76, 73, 63, 91, 86, 82

  • Music: 87, 63, 74, 55, 74, 82, 66, 61, 88, 76, 84

a

Construct a box plot for the Science scores.

b

Construct a box plot for the Music scores.

c

Which subject had the highest score?

11

The marks in an end-of-year exam for a class of students are given below:

52,\, 95,\, 80,\, 56,\, 59,\, 80,\, 86,\, 77,\, 80,\, 81,\, 78,\, 64,\, 84,\, 66,\, 96,\, 90

a

Construct a box plot for the data.

b

Calculate the interquartile range.

c

What percentage of marks lie in the range 85 to 96?

d

Which values do the lowest 75\% of scores lie between?

12

In training, a fighter pilot measures the number of seconds he blacks out over a number of flights. He constructs the following box and whisker plot:

As long as the pilot is not unconscious for more than 7 seconds, he will be safe to fly.

The pilot concludes that he is safe to fly all the time. Explain why his conclusion is incorrect.

Seconds
0
1
2
3
4
5
6
7
8
9
10
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Outcomes

VCMSP350

Construct and interpret box plots and use them to compare data sets.

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