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

Exam code: 0580 & 0980

1 hour22 questions
1
Sme Calculator
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
Sme Calculator
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
Sme Calculator
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<v40

40<v50

50<v80

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
Sme Calculator
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
Sme Calculator
4 marks

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

Temperature (°C)

0<t10

10<t15

15<t20

20<t25

25<t35

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
Sme Calculator
4 marks

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

Time (t seconds)

20<t30

30<t35

35<t40

40<t60

60<t100

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
Sme Calculator
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<m4

4<m6

6<m7

7<m10

Frequency

32

 

 

42

Height of bar on histogram (cm)

1.6

2

1.2

2.8

 

8
Sme Calculator
3 marks

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

Height (h cm)

60<h70

70<h90

90<h100

100<h110

110<h115

115<h125

Frequency

8

26

35

67

28

16

In a histogram showing the information, the height of the bar for the interval  60<h70 is 0.4 cm.

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

115<h125 .................................... cm      
110<h115 .................................... cm      
70<h90 ..................................... cm      

9a
Sme Calculator
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<T30

16

30<T40

18

40<T45

22

45<T50

40

50<T60

21

60<T70

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
Sme Calculator
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<x200

200<x250

250<x300

300<x500

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
Sme Calculator
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<t5

5<t15

15<t30

30<t50

50<t70

Number of people

6

 

27

 

10

1
Sme Calculator
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
Sme Calculator
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<t10

10<t15

15<t20

20<t40

40<t75

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<t10

10<t15

15<t20

20<t40

40<t75

Height of bar (cm)

3.6

14.4

17.6

 

 

3
Sme Calculator
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<t10

10<t15

15<t20

20<t40

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
Sme Calculator
3 marks

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

Age (y years)

15<y25

25<y30

30<y50

50<y80

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<y25 is 7 cm.

Calculate the height of each of the remaining bars.   

25<y30 ........................................ cm     
30<y50 ........................................ cm     
50<y80 ........................................ cm     

5
Sme Calculator
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<m52

52<m62

62<m80

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
Sme Calculator
2 marks

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

Heights (cm)

Frequency

0<h10

10<h25

135

25<h30

25

30<h40

70

40<h55

45

55<h60

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
Sme Calculator
2 marks

Complete the table using the histogram.

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

Calculate an estimate of the mean.

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

2
Sme Calculator
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
Sme Calculator
3 marks

The table gives information about the heights of  150 students.

Height( h cm)

Frequency

140<h150

15

150<h155

30

155<h160

51

160<h165

36

165<h180

18

On the grid, draw a histogram for this information.

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

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

4
Sme Calculator
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
Sme Calculator
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.