Cumulative Frequency Diagrams (Edexcel IGCSE Maths)

Charlotte grows some potatoes.

The table shows information about the weights of her potatoes.

Weight ( grams)	Frequency

Complete the cumulative frequency table.

Weight ( grams)	Cumulative frequency

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

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

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

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

Height ( cm)	Number of students

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

Find an estimate

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

Weekly wage()	Frequency

Complete the cumulative frequency table.

Weekly wage()	Cumulative frequency

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

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

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

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

Time (  minutes)	Frequency

Complete the cumulative frequency table for this information.

Time (  minutes)	Cumulative frequency

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

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

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

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

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

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.

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

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

Mark ()	Cumulative frequency

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

Find the median mark.

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

Find an estimate for the lowest possible pass mark.

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
	7
	26
	24
	14
	7
	2

Complete the cumulative frequency table.

Time taken (t minutes)	Cumulative frequency

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

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

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

One of the 80 customers is chosen at random.

Use your graph to find an estimate for the probability that the time taken by this customer was more than 42 minutes.

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

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

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

Roberto sells the bags of sweets to raise money for charity.
Bags with a weight greater than  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 .

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 ( minutes)	Frequency
	8
	15
	17
	28
	33
	19

Complete the cumulative frequency table.

Time waited ( minutes)	Cumulative Frequency

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

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

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

Using your graph, find an estimate for the percentage of the 120 people who said that they waited longer than 23 minutes before their call was answered.
Show your working clearly.

......................................................% 

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

Time (t minutes)	Frequency
	12
	24
	28
	12
	10
	4

Complete the cumulative frequency table.

Time (t minutes)	Cumulative frequency
	12

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

Any runner who completed the race in a time T minutes such that 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 

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

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.

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.

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.

To be awarded a grade A in the algebra test, a student had to gain a mark greater than 64

Two students are to be selected at random from the 60 students in the group.

Use the graph to find an estimate for the probability that both of these students were awarded a grade A in the algebra test.

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

Roberto sells the bags of sweets to raise money for charity.
Bags with a weight greater than 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 .

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.

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.

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

Clare says,

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

Is Clare correct?
Give a reason for your answer.

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.

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

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

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

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.

To be awarded a grade A in the algebra test, a student had to gain a mark greater than 64

Two students are to be selected at random from the 60 students in the group.

Use the graph to find an estimate for the probability that both of these students were awarded a grade A in the algebra test.

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

Distance travelled (d km)	Cumulative frequency
	17
	32
	57
	70
	76
	80

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

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

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

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

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

For Office , 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 and workers at Office travel from home to work.
Write down two comparisons.

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

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

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

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

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

Clare says,

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

Is Clare correct?
Give a reason for your answer.

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

Estimate the median mass.

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

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.

£...................................

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

Miles per gallon,	Frequency
	6
	16
	28
	10

Draw a cumulative frequency graph.

Use the graph to work out the interquartile range.

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

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

Mark,	Frequency
	9
	16
	20
	8
	7

On the grid, draw a cumulative frequency graph.

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

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

Use the graph to estimate the median annual salary.

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

Complete this cumulative frequency table.

Annual salary, p (£ thousands)	Cumulative frequency

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

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

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

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

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

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

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.

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.

Find

£ ................. [1]

£ ................. [2]

Iqrah says

   15% of these families spent over £120.

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

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 ....................