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Cumulative Frequency (Cambridge O Level Maths): Exam Questions

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1a
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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1b
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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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1c
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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2a
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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2b
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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2c
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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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3
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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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1a
Sme Calculator3 marks

160 students record the amount of time, t hours, they each spend playing computer games in a week.
This information is shown in the cumulative frequency diagram.

cie-igcse-2019-may-jun-p2-tz3-q23a

Use the diagram to find an estimate of

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

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1b
Sme Calculator2 marks

Use the diagram to complete this frequency table.

Time (t hours) 0 less than t less or equal than 2 2 less than t less or equal than 4 4 less than t less or equal than 6 6 less than t less or equal than 8 8 less than t less or equal than 10 10 less than t less or equal than 12
Frequency 20     24 12 4

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2a
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The cumulative frequency graph shows information about the times 80 swimmers take to swim 50 metres.

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

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

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2b
Sme Calculator3 marks

A swimmer has to swim 50 metres in 60 seconds or less to qualify for the swimming team.

The team captain says,

   "More than 25% of swimmers have qualified for the swimming team."

Is the team captain right?
You must show how you got your answer.

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3
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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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
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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
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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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6
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The cumulative frequency diagram shows the marks obtained by 80 students in a Maths test.

q9a-june-2021-4024-21-cambridge-o-level-maths-d

i)
Use the diagram to find an estimate of the median.
[1]
ii)
60% of the students passed the test.
Use the diagram to find the number of marks needed to pass the test.
[2]

Using the information on the diagram, complete the frequency table

Mark (m) 0 less-than or slanted equal to m less than 20 20 less-than or slanted equal to m less than 40 40 less-than or slanted equal to m less than 60 60 less-than or slanted equal to m less than 80 80 less-than or slanted equal to m less than 100
Frequency 8        

[2]

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1a
Sme Calculator2 marks

The cumulative frequency graphs show information about the times taken by 100 male runners and by 100 female runners to finish the London marathon. 

q6-hrd-6-4-cumulative-frequency-edexcel-gcse-maths

A male runner is chosen at random.

Find an estimate for the probability that this runner took less than 4 hours to finish the London marathon.

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1b
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Use medians and interquartile ranges to compare the distribution of the times taken by the male runners with the distribution of the times taken by the female runners.

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2
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The cumulative frequency graph gives information about the weights, in grams, of 90 bags of sweets.

q11-4ma1-1h-qp-jan21-paper1-igcse-maths

Roberto sells the bags of sweets to raise money for charity.
Bags with a weight greater than d grams are labelled large bags and sold for 3.75 euros each bag.

The total amount of money he receives by selling all the large bags is 93.75 euros.

Find the value of d.

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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
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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
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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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