Maths — Higher, Unit 2 — IGCSE

15 markseasy

1 mark

(a)

The table shows information about the speeds of $100$ lorries.

Speed ( $s$ ) 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 ( $s$ ) 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`

Your answer

2 marks

(b)

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

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

Your answer

2 marks

(c)

Find an estimate for the number of lorries with a speed of more than $90$ km/h.

Your answer

How did you do?/ 5

24 markseasy

2 marks

(a)

There are $200$ workers at a factory. The cumulative frequency table gives information about their ages.

Age ( $a$ 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, draw a cumulative frequency graph for this information.

nov-2014-1ma1-1h-q16

Your answer

2 marks

(b)

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

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

Your answer

How did you do?/ 4

36 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)

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)

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

45 markseasy

1 mark

(a)

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

Mark ( $m$ )	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 ( $m$ )	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`

Your answer

2 marks

(b)

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

Your answer

2 marks

(c)

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

Your answer

How did you do?/ 5

52 markseasy

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.

Your answer

How did you do?/ 2

63 markseasy

1 mark

(a)

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.

Your answer

2 marks

(b)

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

Your answer

How did you do?/ 3

76 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)

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)

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

85 markseasy

1 mark

(a)

The frequency table gives information about the ages of the 80 people in a train carriage.

Age ( $a$ years)	Frequency
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 20$	9
$20 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 30$	19
$30 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 40$	17
$40 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 50$	18
$50 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 60$	13
$60 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 70$	4

Complete the cumulative frequency table.

Age ( $a$ years)	Cumulative frequency
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 20$
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 30$
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 40$
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 50$
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 60$
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 70$

Your answer

2 marks

(b)

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

q11b-paper1hr-nov2020-edexcel-igcse-maths

Your answer

2 marks

(c)

Use your graph to find an estimate for the median age of the people in the train carriage.

........................................... years

Your answer

How did you do?/ 5

92 markseasy

(a)

20 students each record the mass, $p$ grams, of their pencil case. The table below shows the results.

Mass ( $p$ grams)	$0<p\leq50$	$50<p\leq100$	$100<p\leq125$	$125<p\leq150$	$150<p\leq200$
Frequency	$2$	$5$	$4$	$6$	$3$

Use the frequency table to complete the cumulative frequency table.

Mass ( $p$ grams)	$p\leq50$	$p\leq100$	$p\leq125$	$p\leq150$	$p\leq200$
Cumulative frequency					$20$

Your answer

How did you do?/ 2

108 marksmedium

1 mark

(a)

Charlotte grows some potatoes.

The table shows information about the weights of her potatoes.

Weight ( $w$ grams)	Frequency
`100 less than w less-than or slanted equal to 120`	$5$
`120 less than w less-than or slanted equal to 140`	$25$
`140 less than w less-than or slanted equal to 160`	$30$
`160 less than w less-than or slanted equal to 180`	$15$
`180 less than w less-than or slanted equal to 200`	$5$

Complete the cumulative frequency table.

Weight ( $w$ grams)	Cumulative frequency
`100 less than w less-than or slanted equal to 120`
`100 less than w less-than or slanted equal to 140`
`100 less than w less-than or slanted equal to 160`
`100 less than w less-than or slanted equal to 180`
`100 less than w less-than or slanted equal to 200`

Your answer

2 marks

(b)

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

x_jTmCoZ_q7b-medium-6-4-cumulative-frequency-edexcel-gcse-maths

Your answer

2 marks

(c)

Use your graph to find an estimate for the interquartile range.

Your answer

3 marks

(d)

Use your graph to find an estimate for the percentage of Charlotte's potatoes with a weight less than 150 grams.

Your answer

How did you do?/ 8

116 marksmedium

3 marks

(a)

The table below shows information about the heights of 60 students.

Height ( $x$ cm)	Number of students
`140 less than x less-than or slanted equal to 150`	$4$
`150 less than x less-than or slanted equal to 160`	$5$
`160 less than x less-than or slanted equal to 170`	$16$
`170 less than x less-than or slanted equal to 180`	$27$
`180 less than x less-than or slanted equal to 190`	$5$
`190 less than x less-than or slanted equal to 200`	$3$

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

Your answer

3 marks

(b)

TUVVKr2T_q8b-medium-6-4-cumulative-frequency-edexcel-gcse-maths

Find an estimate

i) for the median,

(2 marks)

ii) for the interquartile range.

(1 mark)

Your answer

How did you do?/ 6

127 marksmedium

1 mark

(a)

The grouped frequency table shows information about the weekly wages of $80$ factory workers.

Weekly wage( $\pounds x$ )	Frequency
`100 less than x less-than or slanted equal to 200`	$8$
`200 less than x less-than or slanted equal to 300`	$15$
`300 less than x less-than or slanted equal to 400`	$30$
`400 less than x less-than or slanted equal to 500`	$17$
`500 less than x less-than or slanted equal to 600`	$7$
`600 less than x less-than or slanted equal to 700`	$3$

Complete the cumulative frequency table.

Weekly wage( $\pounds x$ )	Cumulative frequency
`100 less than x less-than or slanted equal to 200`
`100 less than x less-than or slanted equal to 300`
`100 less than x less-than or slanted equal to 400`
`100 less than x less-than or slanted equal to 500`
`100 less than x less-than or slanted equal to 600`
`100 less than x less-than or slanted equal to 700`

Your answer

2 marks

(b)

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

q9b-medium-6-4-cumulative-frequency-edexcel-gcse-maths

Your answer

2 marks

(c)

Use your graph to find an estimate for the interquartile range.

Your answer

2 marks

(d)

Use your graph to find an estimate for the number of workers with a weekly wage of more than £530.

Your answer

How did you do?/ 7

136 marksmedium

1 mark

(a)

The table shows information about the times taken by $100$ people in a fun run.

Time ( $t$ minutes)	Frequency
`20 less than t less-than or slanted equal to 30`	$4$
`30 less than t less-than or slanted equal to 40`	$16$
`40 less than t less-than or slanted equal to 50`	$36$
`50 less than t less-than or slanted equal to 60`	$24$
`60 less than t less-than or slanted equal to 70`	$14$
`70 less than t less-than or slanted equal to 80`	$6$

Complete the cumulative frequency table for this information.

Time ( $t$ minutes)	Cumulative frequency
`20 less than t less-than or slanted equal to 30`
`20 less than t less-than or slanted equal to 40`
`20 less than t less-than or slanted equal to 50`
`20 less than t less-than or slanted equal to 60`
`20 less than t less-than or slanted equal to 70`
`20 less than t less-than or slanted equal to 80`

Your answer

2 marks

(b)

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

q10b-medium-6-4-cumulative-frequency-edexcel-gcse-maths

Your answer

1 mark

(c)

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

Your answer

2 marks

(d)

Use your graph to find an estimate for the number of people who took longer than $63$ minutes.

Your answer

How did you do?/ 6

144 marksmedium

1 mark

(a)

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

q11a-medium-6-4-cumulative-frequency-edexcel-gcse-maths

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

Your answer

1 mark

(b)

Jamil says,
"80 - 40 = 40 so the range of the weights is 40 g."

Is Jamil correct? You must give a reason for your answer.

Your answer

2 marks

(c)

Show that less than 25% of the potatoes have a weight greater than 65 g.

Your answer

How did you do?/ 4

156 marksmedium

2 marks

(a)

The cumulative frequency table shows the marks some students got in a test.

Mark ( $m$ )	Cumulative frequency
`0 less than m less-than or slanted equal to 10`	$8$
`0 less than m less-than or slanted equal to 20`	$23$
`0 less than m less-than or slanted equal to 30`	$48$
`0 less than m less-than or slanted equal to 40`	$65$
`0 less than m less-than or slanted equal to 50`	$74$
`0 less than m less-than or slanted equal to 60`	$80$

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

q12a-medium-6-4-cumulative-frequency-edexcel-gcse-maths

Your answer

1 mark

(b)

Find the median mark.

Your answer

3 marks

(c)

Students either pass the test or fail the test. The pass mark is set so that $3$ times as many students fail the test as pass the test.

Find an estimate for the lowest possible pass mark.

Your answer

How did you do?/ 6

164 marksmedium

1 mark

(a)

The table gives information about the times, in minutes, taken by 80 customers to do their shopping in a supermarket.

Time taken ( t minutes)	Frequency
`0 less than t less-than or slanted equal to 10`	7
`10 less than t less-than or slanted equal to 20`	26
`20 less than t less-than or slanted equal to 30`	24
`30 less than t less-than or slanted equal to 40`	14
`40 less than t less-than or slanted equal to 50`	7
`50 less than t less-than or slanted equal to 60`	2

Complete the cumulative frequency table.

Time taken ( t minutes)	Cumulative frequency
`0 less than t less-than or slanted equal to 10`
`0 less than t less-than or slanted equal to 20`
`0 less than t less-than or slanted equal to 30`
`0 less than t less-than or slanted equal to 40`
`0 less than t less-than or slanted equal to 50`
`0 less than t less-than or slanted equal to 60`

Your answer

2 marks

(b)

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

q12-january-2022-1h-edexcel-igcse-maths

Your answer

1 mark

(c)

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

.................................... minutes

Your answer

How did you do?/ 4

175 marksmedium

2 marks

(a)

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

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

Find an estimate for the median of the weights of these bags of sweets.

...................................................... grams

Your answer

3 marks

(b)

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?/ 5

184 marksmedium

1 mark

(a)

The manager of a call centre asked the 120 people, who rang the call centre last week, how long they each waited before their call was answered.

The table gives information about their replies.

Time waited ( $t$ minutes)	Frequency
$0 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 5$	8
$5 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 10$	15
$10 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 15$	17
$15 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 20$	28
$20 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 25$	33
$25 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 30$	19

Complete the cumulative frequency table.

Time waited ( $t$ minutes)	Cumulative Frequency
$0 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 5$
$0 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 10$
$0 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 15$
$0 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 20$
$0 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 25$
$0 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 30$

Your answer

2 marks

(b)

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

q11b-4ma1-1hr-qp-jan21-paper1-igcse-maths

Your answer

1 mark

(c)

Use your graph to find an estimate for the median of the times waited.

...................................................... minutes

Your answer

How did you do?/ 4

195 marksmedium

1 mark

(a)

The table gives information about the times taken by 90 runners to complete a 10 km race.

Time ( t minutes)	Frequency
$25 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 35$	12
$35 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 45$	24
$45 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 55$	28
$55 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 65$	12
$65 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 75$	10
$75 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 85$	4

Complete the cumulative frequency table.

Time ( t minutes)	Cumulative frequency
$25 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 35$	12
$25 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 45$
$25 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 55$
$25 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 65$
$25 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 75$
$25 < t \text{less} - \text{than} or \text{slanted} \text{equal} to 85$

Your answer

2 marks

(b)

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

q11b-4ma1-1h-qp-nov21-paper1-igcse-maths

Your answer

2 marks

(c)

Any runner who completed the race in a time T minutes such that $42 < T \text{less} - \text{than} or \text{slanted} \text{equal} to 52$ minutes was awarded a silver medal.

Use your graph to find an estimate for the number of runners who were awarded a silver medal.

....................................................... runners

Your answer

How did you do?/ 5

207 marksmedium

1 mark

(a)

The frequency table shows information about the ages of 60 people on a train.

Age ( $a$ years)	Frequency
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 10$	4
$10 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 20$	14
$20 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 30$	17
$30 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 40$	13
$40 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 50$	7
$50 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 60$	3
$60 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 70$	2

Complete the cumulative frequency table.

Age ( $a$ years)	Cumulative frequency
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 10$
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 20$
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 30$
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 40$
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 50$
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 60$
$0 < a \text{less} - \text{than} or \text{slanted} \text{equal} to 70$

Your answer

2 marks

(b)

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

Your answer

2 marks

(c)

Use your graph to find an estimate for the interquartile range of the ages of the 60 people.

Your answer

2 marks

(d)

Use your graph to find an estimate for how many of the 60 people are more than 48 years of age.

Your answer

How did you do?/ 7

214 marksmedium

1 mark

(a)

The cumulative frequency graph shows information about the heights, in centimetres, of 50 plants in a flowerbed.

Graph with cumulative frequency on the y-axis and height in centimetres on the x-axis, showing an upward curve peaking at 50 cumulative frequency.

Use the graph to find an estimate for the median height of these plants.

Your answer

1 mark

(b)

Use the graph to find the frequency for the class interval 30 less than Height less-than or slanted equal to 40

Your answer

2 marks

(c)

Use the graph to find an estimate for the number of plants with a height greater than 35 centimetres.

Your answer

How did you do?/ 4

224 marksmedium

1 mark

The cumulative frequency graph gives information about the times, in seconds, that 80 adults took to log in to an online bank.

Line graph showing cumulative frequency against time in seconds, ranging from 0 to 60 seconds, with frequency increasing from 0 to 80.

Find an estimate for the median time.

Your answer

3 marks

(b)

Work out the percentage of these adults that took longer than 50 seconds to log in. Show your working clearly

Your answer

How did you do?/ 4

234 markshard

(b)

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.

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?/ 4

243 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

253 markshard

(b)

A total of 80 national and international runners took part in a race. The cumulative frequency graph gives information about the times, in minutes, they took for the race.

q12-4ma1-1h-qp-jan20-paper1-igcse-maths

60% of the national runners took 50 minutes or less for the race. No international runner took 50 minutes or less for the race.

Work out an estimate for the number of national runners who took part in the race.

Your answer

How did you do?/ 3

263 markshard

(b)

The cumulative frequency graph shows information about the length, in minutes, of each of 80 films.

q10-paper1h-june2018-edexcel-igcse-maths

Clare says,

“More than 35% of these films are over 120 minutes long.”

Is Clare correct? Give a reason for your answer.

Your answer

How did you do?/ 3

275 markshard

1 mark

(a)

A group of 60 students each sat an algebra test and a geometry test. Each test was marked out of 110

The cumulative frequency graph gives information about the marks gained by the 60 students in the algebra test.

q14-4ma1-2hr-qp-jan22-paper2-igcse-maths

Use the graph to find an estimate for the median mark in the algebra test.

Your answer

1 mark

(b)

Use the graph to find an estimate for the number of students who gained 58 marks or less in the algebra test.

Your answer

2 marks

(c)

Use the graph to find an estimate for the interquartile range of the marks gained in the algebra test.

Your answer

1 mark

(d)

The interquartile range of the marks gained in the geometry test is 9

Luis says

“The students’ marks are more spread out in the algebra test than in the geometry test.”

Is Luis correct? Give a reason for your answer.

Your answer

How did you do?/ 5

287 markshard

2 marks

(a)

The cumulative frequency table gives information about the distance, in kilometres, that each of 80 workers travel from home to work at Office $A$ .

Distance travelled (d km)	Cumulative frequency
$0 < d \text{less} - \text{than} or \text{slanted} \text{equal} to 5$	17
$0 < d \text{less} - \text{than} or \text{slanted} \text{equal} to 10$	32
$0 < d \text{less} - \text{than} or \text{slanted} \text{equal} to 15$	57
$0 < d \text{less} - \text{than} or \text{slanted} \text{equal} to 20$	70
$0 < d \text{less} - \text{than} or \text{slanted} \text{equal} to 25$	76
$0 < d \text{less} - \text{than} or \text{slanted} \text{equal} to 30$	80

On the grid below, draw a cumulative frequency graph for the information in the table.

q12a-4ma1-2h-qp-june21-paper2-igcse-maths

Your answer

1 mark

(b)

Use your graph to find an estimate for the median distance travelled.

....................................................... km

Your answer

2 marks

(c)

Use your graph to find an estimate for the interquartile range of the distances travelled.

....................................................... km

Your answer

2 marks

(d)

For Office $B$ , the median distance workers travel from home to work is 15 km and the interquartile range is 5 km.

Use the information above to compare the distances that workers at Office $A$ and workers at Office $B$ travel from home to work. Write down two comparisons.

Your answer

How did you do?/ 7

295 markshard

1 mark

(a)

The cumulative frequency graph gives information about the waiting times, in minutes, of people with appointments at Hospital A.

q12-4ma1-1hr-qp-jan20-paper1-igcse-maths

Use the graph to find an estimate of the median waiting time at Hospital A.

.........................minutes

Your answer

2 marks

(b)

Use the graph to find an estimate of the interquartile range of the waiting times at Hospital A.

............................... minutes

Your answer

2 marks

(c)

At a different hospital, Hospital B, the median waiting time is 28 minutes and the interquartile range of the waiting times is 19 minutes.

Compare the waiting times at Hospital A with the waiting times at Hospital B.

Your answer

How did you do?/ 5

302 markshard

(a)

The cumulative frequency graph shows information about the length, in minutes, of each of 80 films.

q10-paper1h-june2018-edexcel-igcse-maths

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

....................................................... minutes

Your answer

How did you do?/ 2

314 markshard

1 mark

(a)

The cumulative frequency graph shows information about the masses of 200 apples.

q17-paper-2h-nov-2020-aqa-gcse-maths

Estimate the median mass.

................................grams

Your answer

3 marks

(b)

Apples with mass 90 grams or less cost 32p each.

Apples with mass more than 90 grams cost 39p each. Estimate the total cost of the 200 apples.

£...................................

Your answer

How did you do?/ 4

325 markshard

3 marks

(a)

Here is some information about the miles per gallon of 60 cars.

Miles per gallon, $x$	Frequency
$40 < x \text{less} - \text{than} or \text{slanted} \text{equal} to 50$	6
$50 < x \text{less} - \text{than} or \text{slanted} \text{equal} to 60$	16
$60 < x \text{less} - \text{than} or \text{slanted} \text{equal} to 70$	28
$70 < x \text{less} - \text{than} or \text{slanted} \text{equal} to 80$	10

Draw a cumulative frequency graph.

q22a-paper1h-nov2017-aqa-gcse-maths

Your answer

2 marks

(b)

Use the graph to work out the interquartile range.

...........................miles per gallon

Your answer

How did you do?/ 5

335 markshard

3 marks

(a)

Here is some information about the marks of 60 students in a test.

Mark,	Frequency
	9
$50 < m \text{less} - \text{than} or \text{slanted} \text{equal} to 60$	16
$60 < m \text{less} - \text{than} or \text{slanted} \text{equal} to 70$	20
$70 < m \text{less} - \text{than} or \text{slanted} \text{equal} to 80$	8
$80 < m \text{less} - \text{than} or \text{slanted} \text{equal} to 90$	7

On the grid, draw a cumulative frequency graph.

q19a-paper1h-june2017-aqa-gcse-maths

Your answer

2 marks

(b)

Use your graph to estimate the lowest mark of the top 20% of students.

Your answer

How did you do?/ 5

349 markshard

1 mark

(a)

The cumulative frequency graph summarises the annual salary, p (£ thousands), of the 60 workers in a factory.

q12-paper4-nov2019-ocr-gcse-maths

Use the graph to estimate the median annual salary.

£ ...................................... thousands

Your answer

2 marks

(b)

Complete this cumulative frequency table.

Annual salary, p (£ thousands)	Cumulative frequency
$p \text{less} - \text{than} or \text{slanted} \text{equal} to 10$
$p \text{less} - \text{than} or \text{slanted} \text{equal} to 20$
$p \text{less} - \text{than} or \text{slanted} \text{equal} to 30$
$p \text{less} - \text{than} or \text{slanted} \text{equal} to 50$
$p \text{less} - \text{than} or \text{slanted} \text{equal} to 80$

Your answer

5 marks

(c)

Use the information in the cumulative frequency table to calculate an estimate of the mean annual salary.

£ ...................................... thousands

Your answer

1 mark

(d)

Explain why your estimate of the median is more reliable than your estimate of the mean.

Your answer

How did you do?/ 9

353 markshard

(a)(iii)

The cumulative frequency graph shows the distribution of the heights of members of a rowing club.

q13a-paper4-june2019-ocr-gcse-maths

Calculate the percentage of the members who are at least 180 cm tall.

Your answer

How did you do?/ 3

363 markshard

(b)

The cumulative frequency graph shows information about the marks scored by a group of 80 students in a test.

q15-paper5-nov2018-ocr-gcse-maths

The ratio of the number of students passing the test compared to failing the test is 4 : 1. Find the minimum mark needed to pass the test.

Your answer

How did you do?/ 3

379 markshard

3 marks

(a)

Iqrah carries out a survey of 200 families in the north of England on their weekly spending on food.

The cumulative frequency diagram summarises the results.

q15-paper5-nov2017-ocr-gcse-maths

Find

i) the median,

£ ................. [1]

ii) the interquartile range.

£ ................. [2]

Your answer

2 marks

(b)

Iqrah says

15% of these families spent over £120.

Is her statement correct? State the evidence you have used in making your decision.

Your answer

4 marks

(c)

In a survey of 200 families in the south of England, the median weekly amount spent on food was £84 and the interquartile range was £28.

Make two comparisons between the weekly amounts spent on food in the north of England and the south of England. State the evidence you have used in making your comparisons.

1 ....................

2 ....................

Your answer

How did you do?/ 9