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

The partially completed box plot in Figure 1 shows the distribution of daily mean air temperatures using the data from the large data set for Beijing in 2015.

An outlier is defined as a value

• more than below or

• more than above

The three lowest air temperatures in the data set are 7.6 °C, 8.1 °C and 9.1 °C.

The highest air temperature in the data set is 32.5 °C.

Complete the box plot in Figure 1 showing clearly any outliers.

Using your knowledge of the large data set, suggest from which month the two outliers are likely to have come.

Jiang is studying the variable Daily Mean Pressure from the large data set.

He drew the following box and whisker plot for these data for one of the months for one location using a linear scale but

• he failed to label all the values on the scale

• he gave an incorrect value for the median

Using your knowledge of the large data set, suggest a suitable value for the median.

(You are not expected to have memorised values from the large data set. The question is simply looking for sensible answers.)

Using your knowledge of the large data set, suggest a suitable value for the range.

(You are not expected to have memorised values from the large data set. The question is simply looking for sensible answers.)

A medical researcher is studying the number of hours, , a patient stays in hospital following a particular operation.

The histogram summarises the results for a random sample of 90 patients.

Use the histogram to estimate .

The histogram and its frequency polygon below give information about the weights, in grams, of 50 plums.

Show that an estimate for the mean weight of the 50 plums is 63.72 grams.

Calculate an estimate for the standard deviation of the 50 plums.

Later it was discovered that the scales used to weigh the plums were broken.

Each plum actually weighs 5 grams less than originally thought.

State the effect this will have on the estimate of the standard deviation in part (b).

Give a reason for your answer.

A meteorologist is investigating the Daily Total Rainfall, mm, in Heathrow using a random sample of 120 days from the large data set.

The results are summarised in the table below.

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

A "light-rain" day is defined as a day with rainfall between 1 mm and 5 mm.

Calculate an estimate for the number of "light-rain" days recorded in this sample.

Before producing the grouped frequency table, the meteorologist had to clean the data.

Using your knowledge of the large data set, explain why the daily total rainfall data needed to be cleaned.

The box plot in Figure 1 shows the Daily Mean Wind Speed, knots, for the 31 days in October 2015 in Hurn from the large data set.

Show that the value 13 is an outlier.

The Daily Mean Wind Speed data for Leuchars for the same period (October 2015) is summarised below.

Compare the Daily Mean Wind Speed in Hurn and Leuchars for October 2015.

A meteorologist wants to calculate the mean wind speed for Leuchars. The data in the large data set contains some entries recorded as "n/a".

State what "n/a" represents in the large data set and how the meteorologist should handle these entries.

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.

Taruni is studying the time it takes members of her company to travel to the office.

Taruni decided to ask every member of the company the time, minutes, it takes them to travel to the office.

Taruni’s results are summarised by the box plot below.

Write down the interquartile range for these data.

Rana and David both work for the company and have both moved house since Taruni collected her data.

Rana’s journey to work has changed from 75 minutes to 35 minutes and David’s journey to work has changed from 60 minutes to 33 minutes.

Taruni drew her box plot again and only had to change two values.

Explain which two values Taruni must have changed and whether each of these values has increased or decreased.

The partially completed table and partially completed histogram give information about the ages of passengers on an airline.

There were no passengers aged 90 or over.

Complete the histogram.

Use linear interpolation to estimate the median age.

An outlier is defined as a value greater than .

Given that and , determine, giving a reason, whether or not the oldest passenger could be considered as an outlier.

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 kg.

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

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

A biologist times how long it takes each of 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, , 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 kg round of cheese down a steep yard long hillside. A group of friends participated in the contest and the table below summarises the distances travelled by each before first falling over.

Find how many of the 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 and yards away from the start.

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

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

Use the histogram to find an estimate for

(i) the median mass

(ii) the interquartile range.

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

Wendy is using the large data set to learn about the daily mean wind speeds for Leeming in June 2015. She lists the data below.

Using your knowledge of the large data set, state the units for the values in the table.

An outlier is defined as a value more than below or more than above .

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

The histogram summarises the heights of 256 seedlings two weeks after they were planted.

Use linear interpolation to estimate the median height of the seedlings.

Chris decides to model the frequency density for these 256 seedlings by a curve with equation

where is a constant.

Find the value of .

Using this model, write down the median height of the seedlings.

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

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

The fastest of employees are invited to join an advanced project.

Estimate the highest time of an employee who is invited.

The slowest of employees are offered additional support.

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

There are 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 dB and 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 – group was represented by a bar of width cm and height cm.

Find the width and height of the bar for the – group.

The total area under the histogram is .

Find the number of essays which Mr Shapesphere recorded as taking longer than 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 , and .

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 minutes.

Crystal is given an incomplete box plot showing the lengths of unicorn horns. She also knows that the median length is the midpoint of the minimum and maximum lengths, and that the range is 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 unicorn horns.

Crystal discovers that two masses were recorded incorrectly: kg should have been kg, and kg should have been 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.

The table below shows the daily maximum relative humidity, rounded to the nearest per cent, for Leuchars between June and August .

Using your knowledge of the large data set, explain why roughly of these days contained fog and/or mist.

The data from the table are to be presented on a statistical diagram.

For a histogram, the frequency density for the – class is .

Find the frequency density for the – class.

For a cumulative frequency graph, state the coordinates of all the points that should be plotted.

Explain why an exact box plot cannot be drawn using only the information from the table.