Cumulative frequency graphs

The table gives information about the ages of 80 people in a cinema.

Complete the cumulative frequency table.

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

Use your graph to find an estimate for the percentage of the 80 people who are more than 46 years of age. Give your answer correct to the nearest whole number.

The frequency table gives information about the times, in minutes, that 60 people took to complete a puzzle.

Complete the cumulative frequency table.

On the grid opposite, 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 these people who took more than 45 minutes to complete the puzzle.

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

Find an estimate for the median time.

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

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

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

Use the graph to find the frequency for the class interval 30 Height ≤ 40

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

The table gives information about the times taken by 80 people to run a race.

Time taken (t minutes)	Frequency
50 t 60	15
60 t 70	16
70 t 80	21
80 t 90	14
90 t 100	8
100 t 110	6

Complete the cumulative frequency table.

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

Time taken (minutes)

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

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

The table shows information about the times, in minutes, that 80 patients had to wait to see a doctor.

Time (W minutes)	Frequency
0 W 10	7
10 W 20	10
20 W 30	15
30 W 40	32
40 W 50	16

Complete the cumulative frequency table below.

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

Use your graph to find an estimate for the median.

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

The cumulative frequency graph gives information about the time, in minutes, each of 60 people took to shop in a market.

Use the graph to find an estimate for the median time people took to shop in the market.

Use the graph to find an estimate for the number of people who took longer than 55 minutes to shop in the market.

Use the graph to complete the frequency table to give information about the time, in minutes, each of the 60 people took to shop in the market.

Time taken to shop in the market (m minutes)	Frequency
0 m 10	3
10 m 20	5
20 m 30
30 m 40
40 m 50
50 m 60
60 m 70

The cumulative frequency table shows information about the ages of 60 people who went to a gym on Saturday.

Age (a years)	Cumulative frequency
10 a 20	13
10 a 30	36
10 a 40	42
10 a 50	47
10 a 60	52
10 a 70	56
10 a 80	60

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

Use your graph to find an estimate for the median of the ages of these people.

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

Use your graph to find an estimate for the number of these people who are older than 55 years.

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 t 10	7
10 t 20	26
20 t 30	24
30 t 40	14
40 t 50	7
50 t 60	2

Complete the cumulative frequency table.

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

Time taken (minutes)

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

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.

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

Time (t minutes)	Frequency
25 t 35	12
35 t 45	24
45 t 55	28
55 t 65	12
65 t 75	10
75 t 85	4

Complete the cumulative frequency table.

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 42 T 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.

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

Weight (grams)

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

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.

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 5	8
5 t 10	15
10 t 15	17
15 t 20	28
20 t 25	33
25 t 30	19

Complete the cumulative frequency table.

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

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

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

Age (a years)	Frequency
0 a 20	9
20 a 30	19
30 a 40	17
40 a 50	18
50 a 60	13
60 a 70	4

Complete the cumulative frequency table.

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

Age (a years)

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

The table shows information about the number of minutes each of 120 buses was late last Monday.

Number of minutes late (L)	Frequency
0 < L 10	10
10 < L 20	16
20 < L 30	44
30 < L 40	29
40 < L 50	15
50 < L 60	6

Complete the cumulative frequency table below.

On the grid, 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 buses that were more than 48 minutes late last Monday.

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

Time (minutes)

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

60% of the men took 50 minutes or less for the race. No women took 50 minutes or less for the race.

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

Sandeep recorded the length of time, in minutes, that each of 100 adults went for a walk one Saturday afternoon.

The cumulative frequency table gives information about these times.

Time (t minutes)	Cumulative frequency
30 t 40	6
30 t 50	20
30 t 60	56
30 t 70	84
30 t 80	95
30 t 90	100

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

Use your graph to find an estimate for the median length of time that these adults went for a walk.

One of the 100 adults is chosen at random.

Use your graph to find an estimate for the probability that this adult went for a walk for more than 72 minutes.

The table gives information about the times taken, in minutes, for 80 taxi journeys.

Time taken (t minutes)	Frequency
0 t 5	7
5 t 10	10
10 t 15	12
15 t 20	19
20 t 25	18
25 t 30	14

Complete the cumulative frequency table.

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

Time taken (minutes)

Use your graph to find an estimate for the median.

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

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

Length (minutes)

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

Clare says,

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

Is Clare correct? Give a reason for your answer.

The table shows information about the amount of money spent on holiday by each of 120 families.

Money spent (£m)	Frequency
0 m 100	10
100 m 200	36
200 m 300	34
300 m 400	20
400 m 500	15
500 m 600	5

Write down the modal class.

Complete the cumulative frequency table for the information in the table.

On the grid, 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 families that spent more than £450 on holiday.