Cumulative Frequency & Box Plots (AQA GCSE Maths: Higher): Exam Questions

The students in a class kept a record of the amount of time, in minutes, they spent doing homework last week.

The table shows information about the amount of time the girls spent doing homework last week.

On the grid, draw a box plot for the information in the table.

The box plot below shows information about the amount of time the boys spent doing homework last week.

Compare the amount of time the girls spent doing homework with the amount of time the boys spent doing homework.

Colin took a sample of 80 football players.

He recorded the total distance, in kilometres, each player ran in the first half of their matches on Saturday.

Colin drew this box plot for his results.

Work out the interquartile range.

There were 80 players in Colin's sample.

Work out the number of players who ran a distance of more than 5.6 km.

Colin also recorded the total distance each player ran in the second half of their matches.

He drew the box plot below for this information.

Compare the distribution of the distances run in the first half with the distribution of the distances run in the second half.

The box plot shows information about the number of countries competing in each Winter Olympic Games since 1948

Write down the median.

Work out the interquartile range.

The table below shows information about the number of countries competing in each Summer Olympic Games since 1948

Compare the two distributions.

The box plots give information about the wages of a group of 16 year old workers and a group of 18 year old workers.

Compare the distribution of the wages of the 16 year old workers with the distribution of the wages of the 18 year old workers.

There are 200 workers who are 16 years old.

Work out an estimate for the number of these workers whose wages are £130 or more.

Some students were asked how many times they each used their mobile phones last week.

The box plots give information about the male students' answers and about the female students' answers.

Compare the two distributions represented by the box plots.

The box plot shows information about the distribution of the amounts of money spent by some male students on their holidays.

Work out the interquartile range for the amounts of money spent by these male students.

The table below shows information about the distribution of the amounts of money spent by some female students on their holidays.

On the grid above, draw a box plot for the information in the table.

Chris says,    "The box plots show that the female students spent more money than the male students."

Is Chris correct? Give a reason for your answer.

Charlotte grows some potatoes.

The table shows information about the weights of her potatoes.

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 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.

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

Find an estimate

i) for the median,

[2]

ii) for the interquartile range.

[1]

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

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 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 $100$ people in a fun run.

Complete the cumulative frequency table for this information.

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 $63$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.

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 $3$ 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.

Complete the cumulative frequency table.

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 $d$ 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.

Complete the cumulative frequency table.

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.

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.

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

The times that 48 trains left a station on Monday were recorded.

The cumulative frequency graph gives information about the numbers of minutes the trains were delayed, correct to the nearest minute.

The shortest delay was 0 minutes.
The longest delay was 42 minutes.

On the grid below, draw a box plot for the information about the delays on Monday.

48 trains left the station on Tuesday.

The box plot below gives information about the delays on Tuesday.

Compare the distribution of the delays on Monday with the distribution of the delays on Tuesday.

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

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

Mary says,

“ The longest delay on Tuesday was 33 minutes.

This means that there must be some delays of between 25 minutes and 30 minutes.”

Is Mary right?

You must give a reason for your answer.

Tom recorded the times, in seconds, some boys took to complete an obstacle course.
He drew this box plot for his results.

Tom also recorded the times some girls took to complete the obstacle course. Here are the times, in seconds, for the girls.

Compare the distribution of the times for the boys with the distribution of the times for the girls.

Ben played 15 games of basketball.
Here are the points he scored in each game.

Draw a box plot for this information.

Sam plays in the same 15 games of basketball.

The median number of points Sam scored is 23
The interquartile range of these points is 12
The range of these points is 20

Who is more consistent at scoring points, Sam or Ben?
You must give a reason for your answer.

Here are the times, in seconds, that 15 people waited to be served at Rose's garden centre.

On the grid, draw a box plot for this information.

The box plot below shows the distribution of the times that people waited to be served at Green's garden centre.

Compare the distribution of the times that people waited at Rose's garden centre and the distribution of the times that people waited at Green's garden centre.