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Histograms (Cambridge O Level Maths)

Exam Questions

1 hour22 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
Sme Calculator3 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 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
Sme Calculator4 marks

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
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

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
Sme Calculator2 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 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
Sme Calculator3 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


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
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

Complete this histogram to show the information in the table.

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

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9b
Sme Calculator1 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.

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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

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
Sme Calculator2 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 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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12a
Sme Calculator3 marks

The times some students take to travel to school one morning are shown in the table.
The time is recorded in minutes.

Time (t minutes)  5 < t ⩽ 10  10 < t ⩽ 20  20 < t ⩽ 25 25 < t ⩽ 30  30 < t ⩽ 60
Frequency  x  16 29 20 15

On the grid, complete the histogram to represent this information.

q17-specimen-paper1-2025-4024-01-cambridge-o-level-maths-d

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12b
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Jamila says the histogram shows that there are the same number of students in the  5 < t ⩽10 group as in the 10 < t ⩽ 20 group.

Explain why she is wrong.

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1
Sme Calculator2 marks

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
Sme Calculator3 marks

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
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

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
Sme Calculator3 marks

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
Sme Calculator2 marks

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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