Histograms (Cambridge (CIE) IGCSE Maths: Extended): Exam Questions

Exam code: 0580 & 0980

1 hour22 questions
1
3 marks

The heights are also shown in the frequency table.

Height (h cm)

 0 <h ⩽20

20 <h ⩽30

30 < h ⩽ 40

40 < h ⩽ 80

Frequency

120

80

124

76

Complete the histogram to show this information.

q16b-paper2-spec2025-cie-igcse-further-maths
2
2 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

A histogram is drawn to show the information in the frequency table.
The height of the bar for the interval 60 < t ≤ 100 is 10.8 cm.

Calculate the height of the bar for the interval 160 < t ≤ 220.

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

3
3 marks

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<v≤40

40<v≤50

50<v≤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

 

4
4 marks

200 students estimate the total area, A m2, of the windows in a 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

Complete the histogram to show the information in the table.

cie-igcse-spec-p4-q2bii-histogram
5
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

Complete the histogram to show the information in the table.

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

 

6
4 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

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

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

 

7
2 marks

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<m≤4

4<m≤6

6<m≤7

7<m≤10

Frequency

32

 

 

42

Height of bar on histogram (cm)

1.6

2

1.2

2.8

 

8
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

In a histogram showing the information, the height of the bar for the interval  60<h≤70 is 0.4 cm.

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

115<h≤125 .................................... cm      
110<h≤115 .................................... cm      
70<h≤90 ..................................... cm      

9a
4 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

Complete this histogram to show the information in the table.

cie-igcse-2018-oct-nov-p4-tz2-q9aii
9b
1 mark

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.

10
4 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

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

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

11
2 marks

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<t≤5

5<t≤15

15<t≤30

30<t≤50

50<t≤70

Number of people

6

 

27

 

10

1
2 marks

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

Height, h cm

0 < h ≤ 10

10 < h ≤ 20

20 < h ≤ 30

30 < h ≤ 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 < h ≤ 20 is 7.2 cm.

Calculate the height of the bar representing the interval 30 < h ≤ 50.

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

2
3 marks

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

Time (t seconds)

0<t≤10

10<t≤15

15<t≤20

20<t≤40

40<t≤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<t≤10

10<t≤15

15<t≤20

20<t≤40

40<t≤75

Height of bar (cm)

3.6

14.4

17.6

 

 

3
3 marks

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<t≤10

10<t≤15

15<t≤20

20<t≤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
4
3 marks

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

Age (y years)

15<y≤25

25<y≤30

30<y≤50

50<y≤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<y≤25 is 7 cm.

Calculate the height of each of the remaining bars.   

25<y≤30 ........................................ cm     
30<y≤50 ........................................ cm     
50<y≤80 ........................................ cm     

5
4 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<m≤52

52<m≤62

62<m≤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
6a
2 marks

The table and histogram shows information about the heights of plants in a garden.

Heights (cm)

Frequency

0<h≤10

10<h≤25

135

25<h≤30

25

30<h≤40

70

40<h≤55

45

55<h≤60

Bar chart with two bars; first bar at 2 frequency density, 0-10 seconds; second bar at 5 frequency density, 30-40 seconds; x-axis is time in seconds.

Complete the histogram.

6b
2 marks

Complete the table using the histogram.

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

Calculate an estimate of the mean.

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

2
3 marks

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.

3a
3 marks

The table gives information about the heights of  150 students.

Height( h cm)

Frequency

140<h⩽150

15

150<h⩽155

30

155<h⩽160

51

160<h⩽165

36

165<h⩽180

18

On the grid, draw a histogram for this information.

q2-veryhard-6-3-histograms-edexcel-gcse-maths
3b
2 marks

Work out an estimate for the fraction of the students who have a height between  150 cm and  170 cm.

4
4 marks

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]

5
4 marks

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∘.
Work out the value of x.