IGCSEMaths: ExtendedCIEExam Questions4. Probability & Statistics4.7 Cumulative Frequency & Box Plots

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First teaching 2021

Last exams 2024

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Cumulative Frequency & Box Plots (CIE IGCSE Maths: Extended)

Exam Questions

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4.7 Cumulative Frequency & Box Plots

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4.7 Cumulative Frequency & Box Plots

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1
Sme Calculator2 marks

cie-igcse-2020-oct-nov-p4-tz1-q3a

The box-and-whisker plots show the times spent exercising in one week by a group of women and a group of men.

Below are two statements comparing these times.
For each one, write down whether you agree or disagree, giving a reason for your answer.

Statement Agree or disagree Reason
On average, the women spent less time exercising than the men.    
The times for the women show less variation than the times for the men.     

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2
Sme Calculator3 marks

The average speeds, in km/h, of cars travelling along a road are recorded.
The box-and-whisker plot shows this information.

cie-igcse-2020-oct-nov-p4-tz3-q3a

Find

i)
the lowest speed recorded,
 
 ........................................ km/h [1]
ii)
the median,
 
 ........................................ km/h [1]
iii)
the interquartile range.
 
 ........................................ km/h [1]

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3
Sme Calculator2 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

Use the frequency table to complete the cumulative frequency table.

Mass
(p grams)		 space p less or equal than 50 space p less or equal than 100 space p less or equal than 125 space p less or equal than 150 space p less or equal than 200
Cumulative frequency         20

 

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4a
Sme Calculator1 mark

Sue works for a company that delivers parcels.

One day the company delivered space 80 spaceparcels.
The table shows information about the weights, in kg, of these parcels.

Weight ( bold italic w kg) Frequency
0 less than w less-than or slanted equal to 1 19
1 less than w less-than or slanted equal to 2 17
2 less than w less-than or slanted equal to 3 15
3 less than w less-than or slanted equal to 4 12
4 less than w less-than or slanted equal to 5 10
5 less than w less-than or slanted equal to 6 7

Complete the cumulative frequency table.

Weight ( bold italic w kg) Cumulative frequency
0 less than w less-than or slanted equal to 1  
0 less than w less-than or slanted equal to 2  
0 less than w less-than or slanted equal to 3  
0 less than w less-than or slanted equal to 4  
0 less than w less-than or slanted equal to 5  
0 less than w less-than or slanted equal to 6  

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4b
Sme Calculator2 marks

On the grid opposite, draw a cumulative frequency graph for your table.

PLKM_EeP_q7b-easy-6-4-cumulative-frequency-edexcel-gcse-maths

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4c
Sme Calculator3 marks

Sue says,

   "75 % of the parcels weigh less than 3.4 kg."

Is Sue correct?
You must show how you get your answer.

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5a
Sme Calculator1 mark

The table gives information about the marks gained by some students in an exam.

Mark (bold italic m) Frequency
0 less than m less-than or slanted equal to 20 40
20 less than m less-than or slanted equal to 40 70
40 less than m less-than or slanted equal to 60 60
60 less than m less-than or slanted equal to 80 15
80 less than m less-than or slanted equal to 100 10
100 less than m less-than or slanted equal to 120 5

Complete the cumulative frequency table for this information.

Mark (bold italic m) Cumulative frequency
0 less than m less-than or slanted equal to 20  
0 less than m less-than or slanted equal to 40  
0 less than m less-than or slanted equal to 60  
0 less than m less-than or slanted equal to 80  
0 less than m less-than or slanted equal to 100  
0 less than m less-than or slanted equal to 120  

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5b
Sme Calculator2 marks

On the grid, draw a cumulative frequency graph for your table.

fP8vbTAQ_q8c-easy-6-4-cumulative-frequency-edexcel-gcse-maths

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5c
Sme Calculator2 marks

Use your graph to find an estimate for the number of students who gained a mark of more than 54

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6
Sme Calculator2 marks

The cumulative frequency graph shows some information about the heights, in cm, of 60 students.

vzb~QiEm_q9-easy-6-4-cumulative-frequency-edexcel-gcse-maths

Work out an estimate for the number of these students with a height greater than 160 cm.

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7a
Sme Calculator1 mark

The cumulative frequency graph shows information about the weights of 60 apples.

L~Se3n4d_q10a-easy-6-4-cumulative-frequency-edexcel-gcse-maths

Use the graph to find an estimate for the median weight.

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7b
Sme Calculator2 marks

Use the graph to find an estimate for the interquartile range of the weights.

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8a
Sme Calculator1 mark

The grouped frequency table gives information about the times, in minutes, that 80 office workers take to get to work. 

Time (bold italic t minutes) Frequency
0 less than t less-than or slanted equal to 20 5
20 less than t less-than or slanted equal to 40 30
40 less than t less-than or slanted equal to 60 20
60 less than t less-than or slanted equal to 80 15
80 less than t less-than or slanted equal to 100 8
100 less than t less-than or slanted equal to 120 2

Complete the cumulative frequency table.

Time (bold italic t minutes) Cumulative frequency
0 less than t less-than or slanted equal to 20  
0 less than t less-than or slanted equal to 40  
0 less than t less-than or slanted equal to 60  
0 less than t less-than or slanted equal to 80  
0 less than t less-than or slanted equal to 100  
0 less than t less-than or slanted equal to 120  

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8b
Sme Calculator2 marks

On the grid, draw the cumulative frequency graph for this information.

q11b-easy-6-4-cumulative-frequency-edexcel-gcse-maths

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8c
Sme Calculator3 marks

Use your graph to find an estimate for the percentage of these office workers who take more than space 90 spaceminutes to get to work.

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1
Sme Calculator6 marks

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

cie-igcse-2020-oct-nov-p4-tz2-q4a

Use the cumulative frequency diagram to find an estimate of

i)
the median,
 
 ............................................ cm [1]
ii)
the interquartile range,
 
............................................ cm [2]

iii)
the 60th percentile,

 ............................................ cm [1]
iv)
the number of plants with a height greater than 40cm.
 
[2]

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2a
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

i)

Use the frequency table to complete the cumulative frequency table.

Speed
(v km/h)		 v less or equal than 20 v less or equal than 40 v less or equal than 45 v less or equal than 50 v less or equal than 60 v less or equal than 80
Cumulative Frequency 16 50     196 200

 

[1]

ii)

On the grid, draw a cumulative frequency diagram.

cie-igcse-2020-may-jun-p4-tz2-q3bii 

[3]

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2b
Sme Calculator3 marks

Use your diagram to find an estimate of

i)
the upper quartile,

 

 ........................................ km/h [1]

ii)
the number of cars with a speed greater than 35 km/h.

 

[2]

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3
Sme Calculator5 marks

cie-igcse-2019-oct-nov-p4-tz1-q6a

Use the cumulative frequency diagram to find an estimate for

i)
the median,

............................................. min [1]

ii)
the interquartile range,

............................................. min [2]

iii)
the number of students who took more than 40 minutes.

[2]

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4a
Sme Calculator2 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

Complete the cumulative frequency table below.

Height
(h cm)		 h less or equal than 70 h less or equal than 90 h less or equal than 100 h less or equal than 110 h less or equal than 115 h less or equal than 125
Cumulative Frequency           180

 

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4b
Sme Calculator3 marks

On the grid below, draw a cumulative frequency diagram.

cie-igcse-2018-oct-nov-p4-tz1-q4d

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4c
Sme Calculator6 marks

Use your cumulative frequency diagram to find an estimate of

i)
the interquartile range,

.......................................... cm [2]

ii)
the 70th percentile,

.......................................... cm [2]

iii)
the number of children with height greater than 106 cm.

[2]

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5
Sme Calculator6 marks

A factory recycles metal.
The mass, x tonnes, of metal is measured each day for a number of days.
The cumulative frequency diagram shows the results.
 

cie-igcse-2018-oct-nov-p4-tz3-q5b

i)
For how many days was the mass measured?
 
 

[1]

ii)
Find an estimate of the median.
 
 

....................................... tonnes [1]

iii)
Find an estimate of the upper quartile.
 
 

....................................... tonnes [1]

iv)
Find an estimate of the interquartile range.
 
 

........................................tonnes [1]

v)
Find an estimate of the number of days when the mass was greater than 20 tonnes.
 
 

[2]

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6
Sme Calculator10 marks

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
i)
Complete the cumulative frequency table.

Time
(t minutes)		 t less or equal than 20 t less or equal than 25 t less or equal than 30 t less or equal than 35 t less or equal than 40 t less or equal than 45

Cumulative
frequency

 0 44        

[2]
ii)
On the grid, draw a cumulative frequency diagram to show this information.

HzVc06Br_cie-igcse-2018-may-jun-2-p4-q2bii
[3]
iii)
Find the median time.


......................................... min [1]

iv)
Find the interquartile range.


......................................... min [2]

v)
Find the number of students who took more than 37 minutes to complete the cooking challenge.


[2]

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1a
Sme Calculator5 marks

The heights, 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
i)
Use the frequency table to complete the cumulative frequency table.

Height

(h metres)

 h less or equal than 1.4 h less or equal than 1.5 h less or equal than 1.6 h less or equal than 1.7 h less or equal than 1.8 h less or equal than 1.9
Cumulative frequency 7 25        


[2]

ii)
On the grid, draw a cumulative frequency diagram to show this information.

cie-igcse-2020-may-june-p4-tz1-q1_2c

[3]

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1b
Sme Calculator3 marks

Use your diagram to find an estimate for

i)
the median height,

............................................. m [1]
ii)
the 40th percentile.

............................................. m [2]

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2
Sme Calculator4 marks

Here is some information about the masses of potatoes in a sack:

  • The largest potato has a mass of 174 g.
  • The range is 69 g.
  • The median is 148 g.
  • The lower quartile is 121 g.
  • The interquartile range is 38 g.

 On the grid below, draw a box-and-whisker plot to show this information.

cie-igcse-2020-may-jun-p4-tz3-q3a

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3a
Sme Calculator6 marks

The cumulative frequency diagram shows information about the time taken, t seconds, for a group of girls to each solve a maths problem.

cie-igcse-2019-oct-nov-p4-tz2-q2

Use the cumulative frequency diagram to find an estimate for

i)
the median,

 

.................................................. s [1]

ii)
the interquartile range,

 

.................................................. s [2]

iii)
the 20th percentile,

 

.................................................. s [1]

iv)
the number of girls who took more than 66 seconds to solve the problem.

 

[2]

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3b
Sme Calculator6 marks
i)

Use the cumulative frequency diagram to complete the frequency table.

Time
(t seconds)		 0 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 60 60 less than t less or equal than 80 80 less than t less or equal than 100
Frequency 6       4

 

[2]

ii)
Calculate an estimate of the mean time.

 

.................................................. s [4]

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3c
Sme Calculator3 marks

A group of boys solved the same problem.
The boys had a median time of 60 seconds, a lower quartile of 46 seconds and an upper quartile of 66 seconds.

i)
Write down the percentage of boys with a time of 66 seconds or less.

 

................................................ % [1]

ii)
Howard says

"The boys' times vary more than the girls' times."
Explain why Howard is incorrect.

 

[2]

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4a
Sme Calculator3 marks

The cumulative frequency diagram shows information about the distance, d km, travelled by each of 60 male cyclists in one weekend.

cie-igcse-2019-oct-nov-p4-tz3-q5

Use the cumulative frequency diagram to find an estimate of

i)

the median,

.............................................. km [1]

ii)
the lower quartile,

 

.............................................. km [1]

iii)

the interquartile range.

  
.............................................. km [1]

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4b
Sme Calculator1 mark

For the same weekend, the interquartile range for the distances travelled by a group of female cyclists is 40 km.

Make one comment comparing the distribution of the distances travelled by the males with the distribution of the distances travelled by the females.

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4c
Sme Calculator2 marks

A male cyclist is chosen at random.

Find the probability that he travelled more than 50 km.

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4d
Sme Calculator6 marks
i)
Use the cumulative frequency diagram to complete this frequency table.

Distance (bold italic d km) Number of male cyclists
0 less than d less or equal than 40 18
40 less than d less or equal than 50 9
50 less than d less or equal than 60  
60 less than d less or equal than 70  
70 less than d less or equal than 90  
90 less than d less or equal than 120 2

 

[2]

ii)

Calculate an estimate of the mean distance travelled.
 

.............................................. km [4]

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5
Sme Calculator6 marks

200 students estimate the volume, V space straight m cubed, of a classroom.
The cumulative frequency diagram shows their results.

cie-igcse-spec-p4-q2a-diagram

Use the graph to find an estimate of 

i)
the median,
 
.......................................... m3  [1]
ii)
the interquartile range,
 
.......................................... m3  [2]
iii)
the 60th percentile,
 
 .......................................... m3  [1]
iv)
the number of students who estimate that the volume is greater than 300 m3.
 
[2]

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6a
Sme Calculator5 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
i)

Complete the cumulative frequency table.

Time
(m minutes)		 m less or equal than 10 m less or equal than 40 m less or equal than 60 m less or equal than 90 m less or equal than 100 m less or equal than 120
Cumulative frequency 3 42        

[2]

ii)
On the grid, draw the cumulative frequency diagram.

cie-igcse-2018-march-p4-q7c

[3]

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6b
Sme Calculator7 marks

Use your cumulative frequency diagram to find

i)

the median,
 

 ......................................... min [1]

ii)

the interquartile range,
 

 ......................................... min [2]

iii)

the 90th percentile,
 

 ......................................... min [2]

iv)

the number of people who spend more than 30 minutes in the library.
 

 [2]

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7
Sme Calculator3 marks

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

cie-igcse-2020-oct-nov-p4-tz1-q3biii

 Use the cumulative frequency diagram to find an estimate of  

i)
the 60th percentile,

 .......................................... min [1]
ii)
the number of children who spent more than 3 hours exercising.

 [2]

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8a
Sme Calculator2 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

Complete the cumulative frequency table below.

Amount left parenthesis $ m right parenthesis m less or equal than 5 m less or equal than 10 m less or equal than 20 m less or equal than 30 m less or equal than 50
Cumulative Frequency 16       100

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8b
Sme Calculator3 marks

On the grid, draw the cumulative frequency diagram.

cie-igcse-2019-may-jun-p4-tz2-q9c 

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8c
Sme Calculator5 marks

Use your cumulative frequency diagram to find an estimate for

i)
the median, 
 
$ .............................................. [1]
ii)
the interquartile range, 
 
$ .............................................. [2]
iii)
the number of students who spent more than $25. 
 
[2]

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