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Averages & Range (Cambridge (CIE) IGCSE Maths: Extended)

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Averages & Range

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Averages & Range

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1
Sme Calculator3 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.

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2
Sme Calculator6 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 [2]

v) Work out the mean.

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

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3
Sme Calculator6 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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4
Sme Calculator5 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 = ...............................................     

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1
Sme Calculator3 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.

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2a
Sme Calculator1 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.

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2b
Sme Calculator3 marks

Calculate the mean.

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3
Sme Calculator4 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 less than h less or equal than 1.4

1.4 less than h less or equal than 1.5

1.5 less than h less or equal than 1.6

1.6 less than h less or equal than 1.7

1.7 less than h less or equal than 1.8

1.8 less than h less or equal than 1.9

Frequency

7

18

30

24

27

14

Calculate an estimate of the mean height.

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

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4
Sme Calculator4 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 less than v less or equal than 20

20 less than v less or equal than 40

40 less than v less or equal than 45

45 less than v less or equal than 50

50 less than v less or equal than 60

60 less than v less or equal than 80

Frequency

16

34

62

58

26

4

Calculate an estimate of the mean.  

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

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5
Sme Calculator3 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.

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6
Sme Calculator4 marks

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

Time (t seconds)

20 less than t less or equal than 30

30 less than t less or equal than 35

35 less than t less or equal than 40

40 less than t less or equal than 60

60 less than t less or equal than 100

Frequency

38

27

21

16

18

Calculate an estimate of the mean time.  

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

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7
Sme Calculator4 marks

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

Mass (p grams)

0 less than p less or equal than 50

50 less than p less or equal than 100

100 less than p less or equal than 125

125 less than p less or equal than 150

150 less than p less or equal than 200

Frequency

2

5

4

6

3

Calculate an estimate of the mean mass.  

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

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8
Sme Calculator4 marks

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

Height (h cm)

60 less than h less or equal than 70

70 less than h less or equal than 90

90 less than h less or equal than 100

100 less than h less or equal than 110

110 less than h less or equal than 115

115 less than h less or equal than 125

Frequency

8

26

35

67

28

16

Calculate an estimate of the mean.

Give your answer correct to 1 decimal place.  

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

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9
Sme Calculator4 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 less than T less or equal than 30

16

30 less than T less or equal than 40

18

40 less than T less or equal than 45

22

45 less than T less or equal than 50

40

50 less than T less or equal than 60

21

60 less than T less or equal than 70

3

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

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

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10
Sme Calculator4 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 less than x less or equal than 200

200 less than x less or equal than 250

250 less than x less or equal than 300

300 less than x less or equal than 500

Frequency

8

20

12

12

Calculate an estimate of the mean.

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

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11a
Sme Calculator1 mark

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

 Time (t minutes)

20 less than t less or equal than 25

25 less than t less or equal than 30

30 less than t less or equal than 35

35 less than t less or equal than 40

40 less than t less or equal than 45

 Frequency

44

32

28

12

4

Write down the modal time interval.

...................less than t less or equal than ...................

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11b
Sme Calculator1 mark

Write down the interval containing the median time.

...................less than t less or equal than...................

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11c
Sme Calculator4 marks

Calculate an estimate of the mean time.

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

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12
Sme Calculator4 marks

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

Height, h cm

0 space less than space h space less or equal than space 10

10 space less than space h space less or equal than space 20

20 space less than space h space less or equal than space 30

30 space less than space h space less or equal than space 50

Frequency

2

18

62

38

Calculate an estimate of the mean height.

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

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1
Sme Calculator4 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.

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

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2
Sme Calculator4 marks

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

Time (t s)

0 less than t less or equal than 10

10 less than t less or equal than 15

15 less than t less or equal than 20

20 less than t less or equal than 40

40 less than t less or equal than 75

Frequency

9

18

22

30

21

Calculate an estimate of the mean time.  

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

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3
Sme Calculator4 marks

The table shows the amount of money, $ x, given to a charity by each of 60 people.

Amount ($ x)

0 less than x less or equal than 20

20 less than x less or equal than 25

25 less than x less or equal than 35

35 less than x less or equal than 50

50 less than x less or equal than 100

Frequency

21

16

6

10

7

  Calculate an estimate of the mean.  

$................................................

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4
Sme Calculator4 marks

Bob asked each of 40 spacefriends how many minutes they took to get to work.
The table shows some information about his results.

Time taken (m minutes)

Frequency

0 less than m less-than or slanted equal to 10

3

10 less than m less-than or slanted equal to 20

8

20 less than m less-than or slanted equal to 30

11

30 less than m less-than or slanted equal to 40

9

40 less than m less-than or slanted equal to 50

9

Work out an estimate for the mean time taken.

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5
Sme Calculator4 marks

Sumeet records the times, in minutes, for 40 runners to finish a half marathon.
Information about these times is shown in the table.

Time (bold italic t minutes)

Frequency

60 less than t less-than or slanted equal to 90

10

90 less than t less-than or slanted equal to 120

14

120 less than t less-than or slanted equal to 150

9

150 less than t less-than or slanted equal to 180

5

180 less than t less-than or slanted equal to 210

2

Calculate an estimate for the mean time.

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6
Sme Calculator4 marks

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

Time (t minutes)

0 space less than space t space less or equal than space 60

60 space less than space t space less or equal than space 100

100 space less than space t space less or equal than space 160

160 space less than space t space less or equal than space 220

220 space less than space t space less or equal than space 320

Frequency

41

24

23

8

4

Calculate an estimate of the mean time.

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

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7
Sme Calculator4 marks

200 students estimate the total area, A space straight m squared, of the windows in the classroom.
The table shows their results.

Area (Am2)

20 space less than space A space less or equal than space 60

60 space less than space A space less or equal than space 100

100 space less than space A space less or equal than space 150

150 space less than space A space less or equal than space 250

Frequency

32

64

80

24

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

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

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8
Sme Calculator4 marks

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

Temperature (t°C)

0 less than t less or equal than 10

10 less than t less or equal than 15

15 less than t less or equal than 20

20 less than t less or equal than 25

25 less than t less or equal than 35

Number of days

50

85

100

120

10

Calculate an estimate of the mean.  

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

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9
Sme Calculator4 marks

100 students were each asked how much money, $ m, they spent in one week.
The frequency table shows the results.

Amount left parenthesis $ m right parenthesis

0 less than m less or equal than 5

5 less than m less or equal than 10

10 less than m less or equal than 20

20 less than m less or equal than 30

30 less than m less or equal than 50

Frequency

16

38

30

9

7

Calculate an estimate of the mean.   

$ .............................................

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10
Sme Calculator5 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 equals.................................................. [3]

ii) Write down the mode.  

[1]

iii) Write down the median.  

[1]

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11
Sme Calculator4 marks

Three sizes of eggs are sold in a shop.
The table shows the number of eggs of each size sold in one day.

Size

Small

Medium

Large

Mass (m grams)

46 less than m less or equal than 52

52 less than m less or equal than 62

62 less than m less or equal than 80

Number of eggs sold

78

180

162

Calculate an estimate of the mean mass.

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

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12
Sme Calculator4 marks

The frequency table shows information about the time, m minutes, that each of 160 people spend in a library.

Time (m minutes)

0 less than m less or equal than 10

10 less than m less or equal than 40

40 less than m less or equal than 60

60 less than m less or equal than 90

90 less than m less or equal than 100

100 less than m less or equal than 120

Frequency

3

39

43

55

11

9

Calculate an estimate of the mean time spent in the library.  

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

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