IGCSEMathsCambridge (CIE)International MathsExtendedExam QuestionsStatisticsAverages, Ranges & Comparing Data

Averages, Ranges & Comparing Data (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

Exam code: 0607

2 hours41 questions

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Averages, Ranges & Comparing Data

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Hard
1
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5 marks

Roberto records the value of each of the coins he has at home. The table shows the results.

Value (cents)

1

2

5

10

20

50

Frequency

3

1

3

2

4

2

i) Find the range.

........................................... cents [1]

ii) Find the mode.

........................................... cents [1]

iii) Find the median.

........................................... cents [1]

iv) Work out the total value of Roberto’s coins.

........................................... cents [1]

v) Work out the mean.

........................................... cents [1]

How did you do?

2
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4 marks

The test scores of 14 students are shown below.

21

21

23

26

25

21

22

20

21

23

23

27

24

21

Find the range, mode, median and mean of the test scores.  

Range = ....................................................     
Mode = ....................................................     
Median = ....................................................     
Mean = ....................................................      

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3
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3 marks

The students in Class A and in Class B take the same examination.

The lowest score in Class A is 39
The range of scores for Class A is 57
The lowest score in Class B is 33
The range of scores for Class B is 60

Find the range of scores for all the students in both classes.

How did you do?

4
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3 marks

A teacher records the number of days each of the 24 students in her class are absent.
The frequency table shows the results.

Number of days

0

1

2

3

4

5

Frequency

10

8

3

2

0

1

Find the mode, the median and the mean.

Mode = ...............................................     
Median = ...............................................     
Mean = ...............................................     

How did you do?

5
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2 marks

The table shows the marks scored by 40 students in a test.

Mark

5

6

7

8

9

10

Frequency

8

5

11

7

5

4

Calculate the mean mark.

How did you do?

6a
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1 mark

40 people were asked how many times they visited the cinema in one month.
The table shows the results.

Number of cinema visits

0

1

2

3

4

5

6

7

Frequency

5

5

6

6

7

3

6

2

Find the mode.

How did you do?

6b
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2 marks

Calculate the mean.

How did you do?

7
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2 marks

The table shows the marks scored by some students in a test.

Mark

5

6

7

8

9

10

Frequency

8

2

12

2

0

1

Calculate the mean mark.

How did you do?

1
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2 marks

100 students each cut a piece of string.
Each student then measures the length, x cm, of their piece of string.
The results are shown in the table.

Length (x cm)

9<x≤10

10<x≤10.5

10.5<x≤11

11<x≤12.5

12.5<x≤15

Frequency

7

48

35

6

4

Calculate an estimate of the mean

.......................................... cm

How did you do?

2
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2 marks

The heights, h metres, of the 120 boys in an athletics club are recorded.
The table shows information about the heights of the boys.

Height

(h metres)

1.3<h≤1.4

1.4<h≤1.5

1.5<h≤1.6

1.6<h≤1.7

1.7<h≤1.8

1.8<h≤1.9

Frequency

7

18

30

24

27

14

Calculate an estimate of the mean height.

............................................. m

How did you do?

3
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2 marks

The speed, v km/h, of each of 200 cars passing a building is measured.  The table shows the results.

Speed (v km/h)

0<v≤20

20<v≤40

40<v≤45

45<v≤50

50<v≤60

60<v≤80

Frequency

16

34

62

58

26

4

Calculate an estimate of the mean.  

 ........................................ km/h

How did you do?

4
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2 marks

The table shows the time, t seconds, taken by each of 120 boys to solve a puzzle.

Time (t seconds)

20<t≤30

30<t≤35

35<t≤40

40<t≤60

60<t≤100

Frequency

38

27

21

16

18

Calculate an estimate of the mean time.  

............................................. s

How did you do?

5
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2 marks

20 students each record the mass, p grams, of their pencil case. The table below shows the results.

Mass (p grams)

0<p≤50

50<p≤100

100<p≤125

125<p≤150

150<p≤200

Frequency

2

5

4

6

3

Calculate an estimate of the mean mass.  

................................................ g

How did you do?

6
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3 marks

A school nurse records the height, h cm, of each of 180 children. The table shows the information.

Height (h cm)

60<h≤70

70<h≤90

90<h≤100

100<h≤110

110<h≤115

115<h≤125

Frequency

8

26

35

67

28

16

Calculate an estimate of the mean.

Give your answer correct to 1 decimal place.  

.......................................... cm

How did you do?

7
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3 marks

The table shows the amount of time, T minutes, 120 people each spend in a supermarket one Saturday.

Time (T minutes)

Number of people

10<T≤30

16

30<T≤40

18

40<T≤45

22

45<T≤50

40

50<T≤60

21

60<T≤70

3

Use the midpoints of the intervals to calculate an estimate of the mean.

 ......................................... min

How did you do?

8
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2 marks

A factory recycles metal.
The mass, x tonnes, of metal is measured each week.
The table shows the results for 52 weeks.

Mass (x tonnes)

100<x≤200

200<x≤250

250<x≤300

300<x≤500

Frequency

8

20

12

12

Calculate an estimate of the mean.

....................................... tonnes

How did you do?

9a
1 mark

The time taken for each of 120 students to complete a cooking challenge is shown in the table.

 Time (t minutes)

20<t≤25

25<t≤30

30<t≤35

35<t≤40

40<t≤45

 Frequency

44

32

28

12

4

Write down the modal time interval.

...................<t≤ ...................

How did you do?

9b
1 mark

Write down the interval containing the median time.

...................<t≤...................

How did you do?

9c
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2 marks

Calculate an estimate of the mean time.

......................................... min

How did you do?

10
1 mark

The information below summarises data regarding the heights of plants, measured in centimetres.

Height, h cm

0 < h ≤ 10

10 < h ≤ 20

20 < h ≤ 30

30 < h ≤ 50

Frequency

2

18

62

38

Calculate an estimate of the mean height.

............................................ cm

How did you do?

1
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5 marks

The frequency table shows information about the number of books read by some students in a reading marathon.

Number of books read

1

2

3

4

5

6

7

8

Frequency

2

2

16

10

9

4

x

2

i) The mean number of books read is 4.28.  

Find the value of x.  

x=.................................................. [3]

ii) Write down the mode.  

[1]

iii) Write down the median.  

[1]

How did you do?

2
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3 marks

The height, h cm, of each of 100 students is measured.
The table shows the results.

Height (h cm)

100 < h ⩽ 150

150 < h ⩽ 160

160 < h ⩽ 165

165 < h ⩽ 185

Frequency

7

30

41

22

Calculate an estimate of the mean.

Show all your working clearly

.......................................... cm

How did you do?

3
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3 marks

The table shows information about the times, t seconds, taken by each of 100 students to solve a puzzle.

Time (t s)

0<t≤10

10<t≤15

15<t≤20

20<t≤40

40<t≤75

Frequency

9

18

22

30

21

Calculate an estimate of the mean time.  

Show all your working clearly.

............................................... s

How did you do?

4
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3 marks

The frequency table shows the times, t minutes, each of 100 children spent exercising in one week.

Time (t minutes)

0 < t ≤ 60

60 < t ≤ 100

100 < t ≤ 160

160 < t ≤ 220

220 < t ≤ 320

Frequency

41

24

23

8

4

Calculate an estimate of the mean time.

.......................................... min

How did you do?

5
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3 marks

200 students estimate the total area, A m2, of the windows in the classroom.
The table shows their results.

Area (Am2)

20 < A ≤ 60

60 < A ≤ 100

100 < A ≤ 150

150 < A ≤ 250

Frequency

32

64

80

24

Calculate an estimate of the mean.
You must show all your working.   

.......................................... m2 

How did you do?

6
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4 marks

During one year the midday temperatures, t°C, in Zedford were recorded.
The table shows the results.

Temperature (t°C)

0<t≤10

10<t≤15

15<t≤20

20<t≤25

25<t≤35

Number of days

50

85

100

120

10

Calculate an estimate of the mean.
You must show all your working.  

............................................... °C

How did you do?