Edexcel GCSE Statistics Paper 2 Higher June 2022 question paper 1ST0/2H

Tomasz found information about the weather on the Isle of Skye for the 31 days of May 2019 and the 31 days of July 2019

The table gives, for the Isle of Skye, some information about the number of days with rainfall during May.

Using the information in the table, find the number of days with rainfall in May 2019 You must show your working.

The relative risk of rainfall for a day in July compared with a day in May is 1.29

Find the number of days with rainfall in July 2019 You must show your working.

Bill investigated the heights of females competing in different sports.

Using data from the internet, he recorded the height, in cm, of each female in a sample of 15 female rugby players and the height, in cm, of each female in a sample of 15 female basketball players.

He drew the box plot below for the recorded heights of the 15 female basketball players.

(Source: englandrugby.com, gbbasketball.com)

The table gives information about the recorded heights of the 15 female rugby players.

Using the information in the table, draw on the grid above a box plot for the recorded heights of the 15 female rugby players.

Compare the two distributions of heights. Give three comparisons and interpret one of your comparisons.

Considering the method that Bill used to collect his data, comment on the reliability of your comparisons in part (b).

Irina is investigating whether the percentage of the population of a country living in urban areas has an effect on the life expectancy in that country.

Suggest a hypothesis Irina could use for her investigation.

Irina collected the following information about 10 countries.

The Urban population (%) refers to the percentage of the population of the country who live in urban areas.

Irina used statistical software to draw a scatter diagram for the information in the table.

Give a reason why a scatter diagram is an appropriate diagram to use.

For this investigation, which variable is the explanatory variable? Give a reason for your answer.

The scatter diagram from the statistical software is shown below.

Explain, giving a statistical reason, whether or not this scatter diagram supports your hypothesis in part (a).

For these 10 countries, the double mean point of the data is (63.9, 77.8).

Using this information, draw a line of best fit on the scatter diagram.

Using statistical software, Irina finds that the gradient of the line of best fit should be 0.19

Interpret the gradient of the line of best fit.

Irina now finds that South Africa has Urban population 65% and Life expectancy 63 years.

Determine how this information for South Africa fits with the relationship shown in the scatter diagram for the other countries.

A hospital department has three specialist consultants, A, B and C.

The department manager uses 2-digit random numbers to carry out a simulation of the number of consultations per week for each specialist.

According to hospital records, the average number of consultations per week for each specialist is shown in the following table.

The department manager allocates the following 2-digit numbers to each specialist.

Explain why this is an appropriate way for the department manager to allocate the 2-digit numbers.

Also, according to hospital records, the expected total number of consultations in a week for all three specialists is 50

The table below shows the first 45 results from the simulation.

The last five random numbers used by the department manager are

06 74 59 14 29

Using these last five numbers, complete the table below to show the final result of

Each consultation is planned to last no longer than 20 minutes.

According to the simulation, how much more time a week should be allocated to specialist A than to specialist C for all of their consultations?

The department manager decides that the results of her simulation are sufficient for her to plan how much time is needed per week for consultations with each specialist.

Explain why the manager is not correct.

An adventure travel company runs expeditions for groups of 20 people.

The company provides all the food and equipment for these expeditions.

The manager of the company wants to trial a new sports drink to see if it is better than the usual sports drink.

He decides on the following plan.

• Before the expedition each of the 20 people will complete a questionnaire about their fitness and energy levels.

• The 20 people will be divided into two groups of 10 people, a test group and a control group.

• The test group will be given the new sports drink during the expedition.

• The control group will be given the usual sports drink during the expedition.

• After the expedition each of the 20 people will again complete a questionnaire about their fitness and energy levels.

• The energy levels of the two groups after the expedition will be compared.

Explain briefly why a control group should be used.

Explain how the manager could use matched pairs in order to select the people in the two groups.

Assess the reliability of any conclusions that the manager may reach as a result of using his plan.

Give two reasons for your answer.

Paul uses the Petersen capture recapture method in order to find an estimate for the number of trout living in a lake.

To do this, Paul catches an initial sample of 50 trout from the lake and he tags each trout. He then releases the trout back into the lake.

For his second sample, Paul catches a sample of 80 trout from the lake. He finds that 16 of these trout have tags.

Explain what needs to be true about his two samples for them to be valid for the capture recapture method.

Using his results, Paul is able to work out an estimate for the number of trout living in the lake.

Find Paul’s estimate for the number of trout and discuss the validity and the reliability of his estimate.

Andy is investigating the lateness of the trains that arrive at Manchester Piccadilly.

Explain why it is sensible for Andy to collect secondary data for his investigation.

Andy found out data on the lateness of each of 238 trains arriving at Manchester Piccadilly from London on Monday to Friday for one week.

The histogram below was drawn using Andy’s data.

A negative time for a train means that the train arrived early at Manchester Piccadilly.

In the week, 14 trains arrived early.

Find how many of the 238 trains did not arrive more than 10 minutes late at Manchester Piccadilly.

For a long distance journey, such as London to Manchester Piccadilly, a train is only considered to be late when it arrives more than 10 minutes late.

Andy says that more than 1 in 3 trains from London arrive late at Manchester Piccadilly.

Determine whether or not Andy is correct.

You should comment on the reliability of your conclusion.

An engineering production line is set up to produce machine parts with a diameter of 24.50 mm. For quality control, random samples of size 4 are taken and the mean diameter of each sample is calculated. The production line is set so that the sample means should be normally distributed with a mean of 24.50 mm and a standard deviation of 0.005 mm.

Using this information, draw warning lines on the control chart for the sample means. Action lines have already been drawn on the chart.

Upper action line

24.51

Sample mean 24.50 Target line (mm)

24.49

Lower action line

Sample number

A control chart for the sample ranges is also used and is shown below.

0.020

0.015 Upper action line

Sample range 0.010 Upper warning line (mm)

0.005

Sample number

Explain why it is not appropriate to have lower warning lines and lower action lines on the control chart for sample ranges.

The first two samples taken have the following summary statistics.

Plot the summary statistics for these two samples on the control charts.

The machine parts in Sample 3 had the following diameters:

24.498 mm 24.492 mm 24.501 mm 24.509 mm

Use these results to complete both control charts for Sample 3

Describe what action needs to be taken after Sample 3

Three types of sausage are sold in a farm shop, pork, beef and vegan.

The comparative pie charts show information about the number of packs of these sausages sold in the farm shop in May 2015 and in May 2019

The pie charts are drawn accurately and the angles for the vegan sectors are shown.

The radius of the pie chart for May 2019 is greater than the radius of the pie chart for May 2015

Explain what can be deduced from this information.

30 packs of vegan sausages were sold in the farm shop in May 2015

Work out the number of packs of vegan sausages that were sold in the farm shop in May 2019

Changes in the cost of living in the United Kingdom are measured by the consumer price index (CPI).

The table shows the index numbers for June 2019, using 2015 as base year, of the items that contribute to the CPI.

The table also shows the weightings for how the spending by the Jones family is divided between these items.

(Source: Office for National Statistics)

Using 2015 as base year, the CPI for June 2019 was 107.9

Compare the overall change in the cost of living for the Jones family between 2015 and June 2019 with the change in the CPI between 2015 and June 2019

Explain whether or not it is possible to conclude from your calculations that the Jones family is financially better off or worse off in June 2019 as compared with 2015

The mean of the daily winter temperatures and the mean of the daily summer temperatures in the UK have been recorded for each year from 1910 to 2018

This information has been used to model the two distributions of the mean temperatures.

The graphs below give information about these models.

Write down the name of the distribution that is suggested by each of these graphs.

Comment on the difference between the means of these two distributions.

The standard deviation for the distribution of the summer temperatures is 0.8 °C, correct to one decimal place.

Using the graph for the winter temperatures, calculate an estimate for the standard deviation of the distribution of the winter temperatures, correct to one decimal place.

The maximum height of the graph above the temperature axis for the winter temperatures is less than the maximum height of the graph above the temperature axis for the summer temperatures.

Explain why.

Carol says that the standard deviation of daily temperatures in summer for the years from 1910 to 2018 will also be 0.8 °C.

Explain whether or not Carol is correct.

Greta assumes that the means of the daily temperatures each year are independent.

She works out the probability that the means of the daily summer temperatures are greater than 15.6 °C for two consecutive years.

She concludes that this probability is less than 0.001

Using the model for the daily summer temperatures, assess Greta’s conclusion.