Maths — Extended

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Cumulative Frequency (Cambridge International IGCSE Mathematics): Exam Questions

Exam code:0580

13 questions · 95 marks · ≈ 2 hours

Guided practice

16 markseasy

1 mark

(a)

Sue works for a company that delivers parcels.

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

Weight ( $w$ 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 ( $w$ 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`

Your answer

2 marks

(b)

Extract:

| Weight ( w kg) | Frequency | | 0 < w ≤ 1 | 19 | | 1 < w ≤ 2 | 17 | | 2 < w ≤ 3 | 15 | | 3 < w ≤ 4 | 12 | | 4 < w ≤ 5 | 10 | | 5 < w ≤ 6 | 7 |

Complete the cumulative frequency table.

| Weight ( w kg) | Cumulative frequency | | 0 < w ≤ 1 | | | 0 < w ≤ 2 | | | 0 < w ≤ 3 | | | 0 < w ≤ 4 | | | 0 < w ≤ 5 | | | 0 < w ≤ 6 | |

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

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

Your answer

3 marks

(c)

Extract:

The table shows information about the weights, in kg, of these parcels.

| Weight ( w kg) | Frequency | | 0 < w ≤ 1 | 19 | | 1 < w ≤ 2 | 17 | | 2 < w ≤ 3 | 15 | | 3 < w ≤ 4 | 12 | | 4 < w ≤ 5 | 10 | | 5 < w ≤ 6 | 7 | Complete the cumulative frequency table.

| Weight ( w kg) | Cumulative frequency | | 0 < w ≤ 1 | | | 0 < w ≤ 2 | | | 0 < w ≤ 3 | | | 0 < w ≤ 4 | | | 0 < w ≤ 5 | | | 0 < w ≤ 6 | |

Sue says,

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

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

Your answer

How did you do?/ 6

26 markseasy

1 mark

(a)

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

Time ( $t$ 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 ( $t$ 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`

Your answer

2 marks

(b)

Extract:

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

| Time (t minutes) | Frequency | | 0 < t ≤ 20 | 5 | | 20 < t ≤ 40 | 30 | | 40 < t ≤ 60 | 20 | | 60 < t ≤ 80 | 15 | | 80 < t ≤ 100 | 8 | | 100 < t ≤ 120 | 2 |

Complete the cumulative frequency table.

| Time (t minutes) | Cumulative frequency | | 0 < t ≤ 20 | | | 0 < t ≤ 40 | | | 0 < t ≤ 60 | | | 0 < t ≤ 80 | | | 0 < t ≤ 100 | | | 0 < t ≤ 120 | |

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

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

Your answer

3 marks

(c)

Extract:

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

| Time (t minutes) | Frequency | | 0 < t ≤ 20 | 5 | | 20 < t ≤ 40 | 30 | | 40 < t ≤ 60 | 20 | | 60 < t ≤ 80 | 15 | | 80 < t ≤ 100 | 8 | | 100 < t ≤ 120 | 2 |

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

Your answer

How did you do?/ 6

33 markseasy

(b)

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 60^th percentile,

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

ii) the number of children who spent more than 3 hours exercising.

(2 marks)

Your answer

How did you do?/ 3

45 marksmedium

3 marks

(a)

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]

Your answer

2 marks

(b)

Extract:

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 complete this frequency table.

Time ( $t$ hours)	$0<t\leq2$	$2<t\leq4$	$4<t\leq6$	$6<t\leq8$	$8<t\leq10$	$10<t\leq12$
Frequency	20			24	12	4

Your answer

How did you do?/ 5

54 marksmedium

1 mark

(a)

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.

Your answer

3 marks

(b)

Extract:

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

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.

Your answer

How did you do?/ 4

66 marksmedium

(a)

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 60^th percentile,

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

iv) the number of plants with a height greater than 40cm.

(2 marks)

Your answer

How did you do?/ 6

711 marksmedium

2 marks

(c)

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

Height ( $h$ cm)	$60<h\leq70$	$70<h\leq90$	$90<h\leq100$	$100<h\leq110$	$110<h\leq115$	$115<h\leq125$
Frequency	8	26	35	67	28	16

Complete the cumulative frequency table below.

Height ( $h$ cm)	$h\leq70$	$h\leq90$	$h\leq100$	$h\leq110$	$h\leq115$	$h\leq125$
Cumulative Frequency						180

Your answer

3 marks

(d)

Extract:

| Height (h cm) | 60 < h ≤ 70 | 70 < h ≤ 90 | 90 < h ≤ 100 | 100 < h ≤ 110 | 110 < h ≤ 115 | 115 < h ≤ 125 | | Frequency | 8 | 26 | 35 | 67 | 28 | 16 |

| Height (h cm) | h ≤ 70 | h ≤ 90 | h ≤ 100 | h ≤ 110 | h ≤ 115 | h ≤ 125 | | Cumulative Frequency | | | | | | 180 |

On the grid below, draw a cumulative frequency diagram.

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

Your answer

6 marks

(e)

Extract:

A school nurse records the height, ![h] cm, of each of 180 children.

The table shows the information.

Use your cumulative frequency diagram to find an estimate of

i) the interquartile range,

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

ii) the 70^th percentile,

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

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

(2 marks)

Your answer

How did you do?/ 11

810 marksmedium

(b)

The time taken for each of 120 students to complete a cooking challenge is shown in the table.

Time ( $t$ minutes)	$20<t\leq25$	$25<t\leq30$	$30<t\leq35$	$35<t\leq40$	$40<t\leq45$
Frequency	$44$	$32$	$28$	$12$	$4$

i) Complete the cumulative frequency table.

Time ( $t$ minutes)	$t\leq20$	$t\leq25$	$t\leq30$	$t\leq35$	$t\leq40$	$t\leq45$
Cumulative frequency	$0$	$44$

(2 marks)

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

HzVc06Br_cie-igcse-2018-may-jun-2-p4-q2bii

(3 marks)

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 marks)

Your answer

How did you do?/ 10

98 marksmedium

1 mark

The table shows information about battery life of $60$ smartphones on a video-playback test.

Battery life (t hours)	Frequency
$6\leq t<8$	5
$8\leq t<10$	14
$10\leq t<12$	22
$12\leq t<14$	13
$14\leq t<16$	6

Complete the cumulative frequency table for the data.

Battery life (t hours)	Cumulative Frequency
$6\leq t<8$
$6\leq t<10$
$6\leq t<12$
$6\leq t<14$
$6\leq t<16$

Your answer

2 marks

Draw a cumulative frequency graph for the table.

Your answer

3 marks

Work out an estimate for the interquartile range for the data.

Your answer

2 marks

Work out an estimate for the number of phones with a battery life of at least 13 hours.

Your answer

How did you do?/ 8

106 markshard

2 marks

(a)

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.

Your answer

4 marks

(b)

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.

Your answer

How did you do?/ 6

113 markshard

(b)

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 $d$ .

Your answer

How did you do?/ 3

1215 markshard

6 marks

(a)

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 20^th percentile,

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

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

(2 marks)

Your answer

6 marks

(b)

Extract:

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

i) Use the cumulative frequency diagram to complete the frequency table.

Time ( $t$ seconds)	$0<t\leq20$	$20<t\leq40$	$40<t\leq60$	$60<t\leq80$	$80<t\leq100$
Frequency	6				4

(2 marks)

ii) Calculate an estimate of the mean time.

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

Your answer

3 marks

(c)

Extract:

The cumulative frequency diagram shows information about the time taken, t seconds, for a group of girls to each solve a maths problem. Use the cumulative frequency diagram to find an estimate for the median, the interquartile range.

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 marks)

Your answer

How did you do?/ 15

1312 markshard

3 marks

(a)

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]

Your answer

1 mark

(b)

Extract:

iii) the interquartile range.

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

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.

Your answer

2 marks

(c)

Extract:

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

A male cyclist is chosen at random.

Find the probability that he travelled more than 50 km.

Your answer

6 marks

(d)

Extract:

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

i) Use the cumulative frequency diagram to complete this frequency table.

Distance ( $d$ km)	Number of male cyclists
$0<d\leq40$	$18$
$40<d\leq50$	$9$
$50<d\leq60$
$60<d\leq70$
$70<d\leq90$
$90<d\leq120$	$2$

(2 marks)

ii) Calculate an estimate of the mean distance travelled.

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

Your answer

How did you do?/ 12

Weight (

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

Weight (

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

Time (

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

Time (

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

Time (

t

hours)

0<t\leq2

2<t\leq4

4<t\leq6

6<t\leq8

8<t\leq10

10<t\leq12

Frequency

Height (

h

cm)

60<h\leq70

70<h\leq90

90<h\leq100

100<h\leq110

110<h\leq115

115<h\leq125

Frequency

Height (

h

cm)

h\leq70

h\leq90

h\leq100

h\leq110

h\leq115

h\leq125

Cumulative Frequency

180

Time (

t

minutes)

20<t\leq25

25<t\leq30

30<t\leq35

35<t\leq40

40<t\leq45

Frequency

44

32

28

12

4

Time (

t

minutes)

t\leq20

t\leq25

t\leq30

t\leq35

t\leq40

t\leq45

Cumulative frequency

0

44

Battery life (t hours)

Frequency

6\leq t<8

8\leq t<10

10\leq t<12

12\leq t<14

14\leq t<16

Battery life (t hours)

Cumulative Frequency

6\leq t<8

6\leq t<10

6\leq t<12

6\leq t<14

6\leq t<16

Time (

t

seconds)

0<t\leq20

20<t\leq40

40<t\leq60

60<t\leq80

80<t\leq100

Frequency

Distance (

d

km)

Number of male cyclists

0<d\leq40

18

40<d\leq50

9

50<d\leq60

60<d\leq70

70<d\leq90

90<d\leq120

2