Population, Sampling & Collecting Data (Edexcel GCSE Statistics: Higher)

Izzy investigated the ages of female musicians playing different instruments.

Using data from the internet, she recorded the age, in years, of each female in a sample of female 15 guitarists and the age, in years, of each female in a sample of 15 female pianists.

Izzy then compares the distribution of ages of guitarists to the distribution of ages of pianists.

Considering the method that Izzy used to collect her data, comment on the reliability of any comparisons she makes about the distributions.

Alex and Maria are investigating different sports.

Alex wants to find out the favourite sport of the students at his school.

Maria wants to find out which sport generated the most revenue in the United Kingdom last year.

State the population for

(i) Alex’s investigation,

(ii) Maria’s investigation.

Maria plans to collect the information for her investigation from the internet.

State one step that Maria can take to ensure that the information she collects is as reliable as possible.

Alex is deciding between two different sampling methods for his investigation.

Method A: Opportunity sampling by selecting the first 100 students he sees one day.

Method B: Quota sampling by sampling 25 students from each year group.

For each method, give one reason why the method is not random.

Explain which of the two methods Alex should use in order to minimise the bias in his sample. Give a reason for your answer.

The table gives information about the number of books borrowed from a library in 2023.

The table is split by:

• Format (physical or e-book)

• Category (fiction, non-fiction, or children's)

Bridget is going to take a sample of 300 of these borrowed books, stratified by category (fiction, non-fiction, or children's).

Work out how many children's books there should be in the sample.

Describe a scenario when it would not be appropriate to take a sample stratified by category (fiction, non-fiction, or children's).

Bridget could have used a different property of the books in the library to create a stratified sample.

What is this different property?

A tech company organises weekly productivity workshops for groups of 20 employees.

The company provides all necessary resources for these workshops.

The manager wants to test a new time-management technique to see if it is more effective than the current method.

He decides on the following plan:

• Before the workshop, each of the 20 employees will complete a questionnaire about their current productivity and stress levels.

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

• The test group will be trained in the new time-management technique during the workshop.

• The control group will continue with the current time-management method.

• After the workshop, and after a week spent using the time-management techniques for their work, each of the 20 employees will again complete a questionnaire about their productivity and stress levels.

• The productivity and stress levels of the two groups after the workshop and week's work 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 this plan.

Give two reasons for your answer.

Rina and Haruto work in the head office of a chain of hotels.

The room service menu in all of the hotels has recently been updated. Rina and Haruto have been asked to find out the effect of these changes.

They are going to start by finding out what the housekeeping staff think of the new room service menu.

Rina thinks that they should use a cluster sample of housekeeping staff in the hotels. The hotels would be the clusters.

Haruto thinks that they should use judgment sampling. The head of housekeeping for the company would be asked to select suitably experienced housekeeping staff for the judgment sample.

Discuss whether these two sampling methods are suitable for Rina and Haruto to use.

A national chain of bookshops has 88 stores across the United Kingdom with a total of 1800 employees. Each store is categorised as either a large bookshop or a small bookshop.

The directors of the bookshop chain are considering implementing changes to the shop's opening hours. They wish to survey a sample of 180 employees from the total workforce to gather feedback on the proposed changes.

Three possible sampling methods to select the employees for the survey are suggested.

• Method A
  All 1800 employees are assigned a unique number from 0001 to 1800.
  Starting with employee number 5, they select every 10th employee so that the sample includes employees with the numbers 0005, 0015, 0025, … up to 1795.

• Method B
  Each employee in each store receives a raffle ticket, and 10% of the employees in each store are randomly selected by drawing raffle tickets from a box designated for each store.

• Method C
  The directors will choose two employees from each small bookshop and five employees from each large bookshop.

For each of the three methods, identify the sampling method and discuss whether the sampling method is an appropriate way to select the employees to be in the survey.

As part of your discussion, you should also state, with reasons, which of the three sampling methods is the most appropriate method for the directors to use.

A leisure centre wants to investigate the number of times its members have lent their membership card to a friend to access the facilities at the leisure centre, this is against the rules of the membership.

The leisure centre uses a questionnaire.

Here is one of the questions on the questionnaire:

Assess the appropriateness of the method the leisure centre uses.

120 people were surveyed using the questionnaire.

Here are the results for this question.

• 82 people ticked box A

• 38 people ticked box B

Find an estimate for the number of people in the sample of 120 who had lent their membership card to a friend.

A garage has three mechanics, X, Y, and Z.

The garage manager uses 2-digit random numbers to carry out a simulation of the number of repairs completed per week by each mechanic.

According to garage records, the average number of repairs completed per week by each mechanic is shown in the following table.

The manager allocates the following 2-digit numbers to each mechanic in proportion to their average number of repairs.

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

According to the garage's records, the expected total number of repairs in a week for all three mechanics is 50.

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

The last five random numbers used by the garage manager are:

31 51 82 19 11

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

Each repair is planned to last no longer than 2 hours on average.

According to the simulation, how much more time per week should be allocated to mechanic Y than to mechanic Z for all of their consultations?

The garage manager decides that the results of the simulation are sufficient to plan how much time is needed per week for repairs booked in with each mechanic.

Explain why the manager is not correct.