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Cumulative Frequency (Cambridge O Level Maths)

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Cumulative Frequency

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Cumulative Frequency

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1
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Harry grows tomatoes.
This year he put his tomato plants into two groups, group A and group B.

Harry gave fertiliser to the tomato plants in group A.
He did not give fertiliser to the tomato plants in group B.

Harry weighed 60 tomatoes from group A.
The cumulative frequency graph shows some information about these weights.

q4a-hrd-6-4-cumulative-frequency-edexcel-gcse-maths

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

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2
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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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3a
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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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3b
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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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3c
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Use your graph to find an estimate for the number of students who gained a mark of more than 54

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4
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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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5a
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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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5b
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Use the graph to find an estimate for the interquartile range of the weights.

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6a
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A group of 80 students took a physics test.
This table shows the distribution of their marks.

Mark (m) 0 space less than space m space less or equal than space 10 10 space less than space m space less or equal than space 20 20 space less than space m space less or equal than space 30 30 space less than space m space less or equal than space 40 40 space less than space m space less or equal than space 50 50 space less than space m space less or equal than space 60
Frequency 4 12 14 22 18 10

Complete the cumulative frequency table.

Mark (m) m space less or equal than space 10 m space less or equal than space 20 m space less or equal than space 30 m space less or equal than space 40 m space less or equal than space 50 m space less or equal than space 60
Cumulative Frequency            

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6b
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Draw a cumulative frequency curve for this information.

q8b-june-2018-4024-1-cambridge-o-level-maths-d

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6c
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The pass mark for the test is 45.
 Use your cumulative frequency curve to estimate the number of students who passed.

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1a
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There are space 200 spaceworkers at a factory.
The cumulative frequency table gives information about their ages.

Age (bold italic a years) Cumulative frequency
0 less than a less-than or slanted equal to 20 25
0 less than a less-than or slanted equal to 30 70
0 less than a less-than or slanted equal to 40 138
0 less than a less-than or slanted equal to 50 175
0 less than a less-than or slanted equal to 60 186
0 less than a less-than or slanted equal to 70 194
0 less than a less-than or slanted equal to 80 200

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

q6a-easy-6-4-cumulative-frequency-edexcel-gcse-maths

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1b
Sme Calculator2 marks

Graham says,
   "10% of workers at the factory are older than 65"

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

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2a
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The time, t minutes, 80 students each spend completing their homework is recorded.
The cumulative frequency diagram shows the results.

cie-igcse-2018-oct-nov-p2-tz2-q24

Use the cumulative frequency diagram to find an estimate of the median.
 

......................................... min

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2b
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Use the cumulative frequency diagram to find an estimate of the interquartile range.
 

......................................... min

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2c
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Use the cumulative frequency diagram to find an estimate of the number of students who spend more than 40 minutes completing their homework.

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3a
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The cumulative frequency diagram shows information about the time, m minutes, taken by 120 students to complete some homework.

cie-igcse-2018-may-jun-1-p2-q18-again
Use the cumulative frequency diagram to find an estimate of the interquartile range.

......................................min

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3b
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Use the cumulative frequency diagram to find an estimate of the number of students who took more than 50 minutes to complete the homework.

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4a
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The table shows information about the speeds of space 100 spacelorries.

Speed (bold italic s) in km/h Frequency
0 less than s less-than or slanted equal to 20 2
20 less than s less-than or slanted equal to 40 9
40 less than s less-than or slanted equal to 60 23
60 less than s less-than or slanted equal to 80 31
80 less than s less-than or slanted equal to 100 27
100 less than s less-than or slanted equal to 120 8

Complete the cumulative frequency table for this information.

Speed (bold italic s) in km/h Cumulative frequency
0 less than s less-than or slanted equal to 20 2
0 less than s less-than or slanted equal to 40  
0 less than s less-than or slanted equal to 60  
0 less than s less-than or slanted equal to 80  
0 less than s less-than or slanted equal to 100  
0 less than s less-than or slanted equal to 120  

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4b
Sme Calculator2 marks

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

q5a-easy-6-4-cumulative-frequency-edexcel-gcse-maths

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4c
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Find an estimate for the number of lorries with a speed of more than space 90 spacekm/h.

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5a
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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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5b
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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6
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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7
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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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8a
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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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8b
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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9
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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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1
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A student measures the height, h cm, of each of 400 plants.

The cumulative frequency diagram shows the results.

q16a-paper2-spec2025-cie-igcse-further-maths

Use the diagram to find an estimate for

i)
the median

.......................................... cm[1]

ii)
the interquartile range

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

iii)
the 80th percentile

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

iv)
the number of plants with a height greater than 60cm.
[2]

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2a
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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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2b
Sme Calculator3 marks

On the grid, draw the cumulative frequency diagram.

cie-igcse-2019-may-jun-p4-tz2-q9c 

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2c
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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3a
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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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3b
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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