Data Presentation (AQA A Level Maths: Statistics): Exam Questions

A comparison of the masses (in kg) of convertible cars was made using the Large Data Set. A sample of 20 masses was chosen from both the 2002 data and the 2016 data. The masses of the 20 cars in each sample were used to create a box plot for each year. The box plots were labelled Box Plot A and Box Plot B as shown in the diagram below.

Estimate the median of the masses from Box Plot A.

It is claimed that Box Plot B must be incorrectly drawn.

(i) Give a reason why this claim was made.

(ii) Comment on the validity of this claim.

It is claimed that Box Plot B must be from the 2002 data. Give a reason why this claim is correct.

A biologist studying otter populations records the mass, in grams, of each baby otter at a research centre. The data is illustrated in the box and whisker diagram below.

(i) Find the median mass of the otters.

(iii) Find the interquartile range.

The same otters are weighed monthly to track their growth. Summary data on the masses, in grams, of the otters after one month is shown in the table below.

On the grid below, draw a box plot for the information given above.

120 competitors enter an elimination race for charity. Runners set off from the same start running as many laps of the course as possible. Their total distance is tracked and the competitor who runs the furthest over a 6-hour period is the winner.

The distances runners achieved are recorded in the table below.

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

Use your graph to estimate

(i) the median distance run

(ii) the interquartile range.

The total amount of time cleaners spent dealing with unplanned incidents in a supermarket was recorded each day. Data collected over 49 days is summarised in the table below.

On the grid below, draw a histogram to represent this data.

Estimate the number of days that cleaners spent longer than 3 hours dealing with incidents.

Filmworld cinemas collected data on the ages of visitors to their cinemas during a 24-hour period. The incomplete histogram and frequency table show some of the information they collected.

Use the histogram to complete the frequency table.

Use the frequency table to complete the histogram.

Safety officers check the speed of vehicles travelling along a stretch of highway. The cumulative frequency curve below summarises the data for the speeds, in kmph, of 80 vehicles.

Use the graph to estimate the median speed.

The speed limit for this section of road is 80 kmph.

Vehicles travelling above the speed limit are issued with a speeding ticket. Those travelling more than 10% over the speed limit are pulled over.

Use the graph to estimate the percentage of vehicles that the safety officers pull over.

The histogram below shows the masses, in grams, of $80$ apples.

Use the histogram to find an estimate for

(i) the median mass

(ii) the interquartile range.

Given that the lightest apple weighs $41$ g and that the range of masses is $97$ g, draw a box plot to show the distribution of the masses of the apples.

The amounts of time engineers spent dealing with individual faults in a power plant were recorded to the nearest minute. Data on 30 different faults is summarised in the table below.

Give a reason to justify the use of a histogram to represent these data.

On the grid below, draw a histogram to represent the data.

Use your histogram to estimate the proportion of individual faults on which engineers spent longer than three hours.

A teacher took 19 students on an international trip. The incomplete box plot below shows part of the summary of the weights, in kg, of the luggage brought by each student. Each student's luggage weighed a different amount.

The median weight is 4 kg more than the lower quartile, and the range of weights is three times the interquartile range.

Use this information to complete the box plot.

Calculate the proportion of luggage weights which were less than $20$ kg.

Students had to pay an additional fee if the weight of their luggage exceeded $23$ kg.

Find the number of students who had to pay the additional fee.

A biologist times how long it takes each of $80$ mice to find the exit to a maze. Every two and a half minutes she records the number of mice which have found the exit, which she then represents as a cumulative frequency curve.

Based on the graph, state an inequality for the time, $t$, taken by the fastest mouse.

The biologist also recorded the actual times taken by the fastest and slowest mice. She has used this information to begin constructing a box plot to represent the data.

Use the cumulative frequency curve to complete the box plot for the times.

An annual cheese-rolling contest involves participants chasing a $4$ kg round of cheese down a steep $200$ yard long hillside. A group of $60$ friends participated in the contest and the table below summarises the distances travelled by each before first falling over.

Find how many of the $60$ friends made it to the bottom without falling over.

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

The steepest part of the hill is between $100$ and $140$ yards away from the start.

Use your graph to estimate the number of people who fell during this section of the hill.

The cumulative frequency graph below shows the times, in seconds, taken by $160$ employees of a company to complete a training task.

Use your graph to estimate the number of employees whose time is within $5$ seconds of the median time.

The fastest $10\%$ of employees are invited to join an advanced project.

Estimate the highest time of an employee who is invited.

The slowest $5\%$ of employees are offered additional support.

Estimate the lowest time of an employee who is offered support.

There are $180$ dogs at a vet's clinic. The histogram below shows the highest sound level reached by each individual dog's bark, measured in decibels (dB).

State what is represented by the area of each bar in a histogram.

Use the histogram to estimate the number of dogs which had a bark with a highest sound level between $99$ dB and $107$ dB.

Mr Shapesphere, a history teacher, records the time, to the nearest minute, it takes him to mark each student's essay. The times were summarised in a grouped frequency table and an extract is shown below.

A histogram was drawn to represent these data. The $11$–$30$ group was represented by a bar of width $6$ cm and height $4.5$ cm.

Find the width and height of the bar for the $0$–$10$ group.

The total area under the histogram is $60.75{\text{ cm}}^2$.

Find the number of essays which Mr Shapesphere recorded as taking longer than $35$ minutes, to the nearest minute.

The grouped frequency table below contains information about the lengths of time of Susie's calls with her customers. The table was used to draw the cumulative frequency curve also shown below.

Use the graph to find the values of $a$, $b$ and $c$.

Use the graph to estimate the interquartile range of times for Susie's calls.

Use the graph to estimate the percentage of customers whose calls lasted longer than $10$ minutes.

Crystal is given an incomplete box plot showing the lengths of $99$ unicorn horns. She also knows that the median length is the midpoint of the minimum and maximum lengths, and that the range is $2.5$ times as big as the interquartile range.

Complete the diagrams below to show that there are two possible distributions given the information above.

The box plot below shows the masses of the $99$ unicorn horns.

Crystal discovers that two masses were recorded incorrectly: $11$ kg should have been $8$ kg, and $9$ kg should have been $10$ kg.

Explain why at most one feature of the box plot will need to change.

Explain why it is possible that the box plot will remain unchanged when it is fixed.