IGCSEMathsCambridge (CIE)ExtendedExam QuestionsStatisticsHistograms

Histograms (Cambridge (CIE) IGCSE Maths: Extended)

Exam Questions

1 hour21 questions
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1
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The heights are also shown in the frequency table.

Height (h cm)

 0 space less than h space less-than or slanted equal to 20

20 space less than h space less-than or slanted equal to 30

30 space less than space h space less-than or slanted equal to space 40

40 space less than space h space less-than or slanted equal to space 80

Frequency

120

80

124

76

Complete the histogram to show this information.

q16b-paper2-spec2025-cie-igcse-further-maths

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2
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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

A histogram is drawn to show the information in the frequency table.
The height of the bar for the interval 60 space less than space t space less or equal than space 100 is 10.8 cm.

Calculate the height of the bar for the interval 160 space less than space t space less or equal than space 220.

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

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3
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The speed, v km/h, of each of 200 cars passing a building is measured.  
The frequency table shows the results.

Speed (v km/h)

0 less than v less or equal than 40

40 less than v less or equal than 50

50 less than v less or equal than 80

Frequency

50

120

30

On the grid, draw a histogram to show the information in this table.

I5mAMXYu_cie-igcse-2020-may-jun-p4-tz2-q3d

 

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4
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200 students estimate the total area, A space straight m squared, of the windows in a 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

Complete the histogram to show the information in the table.

cie-igcse-spec-p4-q2bii-histogram

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5
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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

Complete the histogram to show the information in the table.

XN6Oh0uk_cie-igcse-2020-may-jun-p4-tz1-q4

 

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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

On the grid, complete the histogram to show the information in the frequency table.

f_VfpVAx_cie-igcse-2019-may-jun-p4-tz3-q6b

 

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7
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Some students each record the mass, m kg, of their school bag.
Adil wants to draw a histogram to show this information.   Complete the table below.

Mass (m kg)

0 less than m less or equal than 4

4 less than m less or equal than 6

6 less than m less or equal than 7

7 less than m less or equal than 10

Frequency

32

 

 

42

Height of bar on histogram (cm)

1.6

2

1.2

2.8

 

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8
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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

In a histogram showing the information, the height of the bar for the interval  60 less than h less or equal than 70 is 0.4 cm.

Calculate the height of the bar for each of the following intervals.  

115 less than h less or equal than 125 .................................... cm      
110 less than h less or equal than 115 .................................... cm      
70 less than h less or equal than 90 ..................................... cm      

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9a
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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

Complete this histogram to show the information in the table.

cie-igcse-2018-oct-nov-p4-tz2-q9aii

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9b
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This histogram shows the amount of time, T minutes, 120 people each spend in the supermarket one Wednesday.

cie-igcse-2018-oct-nov-p4-tz2-q9b

Make a comment comparing the distributions of the times for the two days.

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10
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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

cie-igcse-2018-oct-nov-p4-tz3-q5aii

On the grid, draw a histogram to show the information in the table.

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11
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The histogram shows information about the time, t minutes, spent in a shop by each of 80 people.

cie-igcse-2018-may-jun-2-p2-q13

Complete the frequency table.

Time (t minutes)

0 less than t less or equal than 5

5 less than t less or equal than 15

15 less than t less or equal than 30

30 less than t less or equal than 50

50 less than t less or equal than 70

Number of people

6

 

27

 

10

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1
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The height, h cm, of each of 120 plants is measured. The frequency table shows this information.

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

A histogram is drawn to show the information in the frequency table.
The height of the bar representing the interval 10 space less than space h space less or equal than space 20 is 7.2 cm.

Calculate the height of the bar representing the interval 30 space less than space h space less or equal than space 50.

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

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2
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The table shows information about the times, t seconds, taken by each of 100 students to solve a puzzle.

Time (t seconds)

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

Emmanuel draws a histogram to show this information.
The table shows the heights, in cm, of some of the bars for this histogram.  
Complete the table.

Time (t seconds)

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

Height of bar (cm)

3.6

14.4

17.6

 

 

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3
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The time, t minutes, it takes each of 50 students to travel to school is recorded.
The table shows the results.

Time (t minutes)

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

Frequency

7

19

 16

8

On the grid, complete the histogram to show the information in the table.

cie-igcse-2019-oct-nov-p2-tz3-q23

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4
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The table shows the number of people in different age groups at a cinema.

Age (y years)

15 less than y less or equal than 25

25 less than y less or equal than 30

30 less than y less or equal than 50

50 less than y less or equal than 80

Number of people

35

32

44

12

Dexter draws a histogram to show this information. 
The height of the bar he draws for the group 15 less than y less or equal than 25 is 7 cm.

Calculate the height of each of the remaining bars.   

25 less than y less or equal than 30 ........................................ cm     
30 less than y less or equal than 50 ........................................ cm     
50 less than y less or equal than 80 ........................................ cm     

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5
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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

On the grid, draw a histogram to show the information in the table.

cie-igcse-2018-may-jun-3-p4-q3c

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1
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cie-igcse-2019-oct-nov-p4-tz1-q6c

Calculate an estimate of the mean.

............................................... kg

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2
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The histogram shows information about the weights, in grams, of some plums.

q1-veryhard-6-3-histograms-edexcel-gcse-maths

Work out an estimate for the proportion of these plums with a weight of less than 100 grams.

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3a
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The table gives information about the heights of space 150 spacestudents.

Height( bold italic h cm)

Frequency

140 less than h less-than or slanted equal to 150

15

150 less than h less-than or slanted equal to 155

30

155 less than h less-than or slanted equal to 160

51

160 less than h less-than or slanted equal to 165

36

165 less than h less-than or slanted equal to 180

18

On the grid, draw a histogram for this information.

q2-veryhard-6-3-histograms-edexcel-gcse-maths

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3b
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Work out an estimate for the fraction of the students who have a height between space 150 spacecm and space 170 spacecm.

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4
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The histogram shows information about the time taken by cyclists to finish a cycle race.

q3-veryhard-6-3-histograms-edexcel-gcse-maths

7 cyclists took 80 minutes or less to finish the race.

i) Work out an estimate for the number of cyclists who took more than 105 minutes to finish the race.

[3]

ii) Explain why your answer to part (i) is only an estimate.

[1]

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5
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The histogram gives information about the distribution of the weights of some onions grown by a farmer.

q4-veryhard-6-3-histograms-edexcel-gcse-maths

Onions less than 60 grams in weight are used for pickling. Onions greater than 120 grams in weight are sold at the market. The rest of the onions are sent to a food processing factory.

A pie chart is drawn using the information opposite to show what the farmer does with the onions he grows.

q4-1-veryhard-6-3-histograms-edexcel-gcse-maths

The angle of the sector for the onions sent to the food processing factory is x to the power of ring operator.
Work out the value of x.

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