Types of Data & Sampling (AQA Level 3 Mathematical Studies (Core Maths): Paper 1: Data, Finance, Estimation & Modelling): Exam Questions

Each year the European Union asks each member country to provide data for the volume of landfill waste per person.

What type of data is collected by the European Union?
Tick all boxes that apply

You may use Waste on pages 4 and 5 of the Preliminary Material.

In recent years people have been encouraged to recycle where possible. However, if waste cannot be recycled it is put into a landfill site.

• A new landfill site is to be built for a small town.

• The site will have a hole in the ground and the town’s waste will be put into the hole.

• The site needs to be used for a minimum of 15 years.

Estimate the dimensions of the hole.

Show details of your assumptions and calculations.

Helen is collecting data about school subjects.

One question she will ask students is

“What is your favourite subject at school?”

Which two words describe the type of data Helen will collect for this question?

Tick (✓) one box.

Helen will ask students in Years 7, 8 and 9 in her school.

The table shows the number of students in each year group.

Helen wants to take a stratified sample of 60 students, stratified by year group.

Helen chooses 20 students from each year group for her sample.

Explain why this is not a stratified sample.

Work out the number of students from each year group that should be in a stratified sample of 60

Year 7 __________________________________________
Year 8 __________________________________________
Year 9__________________________________________

Rafiq and Ellen are doing surveys about favourite school lessons.

They each want to take a sample of 75 students from their school.

The table shows the number of students in each year group.

To get his sample of 75, Rafiq asks 15 students from each of the five year groups.

What is the name of this sampling method?

Give one advantage and one disadvantage of Rafiq’s sampling method.

Ellen decides that the number in her sample from each year group should be in proportion to the total number of students in that group.

What is the name of this sampling method?

There are 900 students in the school.

How many more Year 7 students than Year 11 students should Ellen have in her sample?

Mr Berry wants his class to study some data on swimming times.

He collects data from the Internet about two swimming strokes, backstroke and breaststroke.

The table shows the fastest 19 times, in seconds, for the men’s 100m Backstroke at a major championship.

Which two words describe the type of data he has collected?

Tick(✓) your answers.

The table below shows information about the fastest 19 times for the men’s 100m Breaststroke in the same championship.

Complete this table to show the information for the backstroke.

The lowest and highest values have been completed for you.

Draw box and whisker plots to represent the data for the backstroke and breaststroke times.

Make two comparisons of the distribution of times for the swimming strokes.

You should make one comparison based on the averages and one comparison based on the spreads.

Rasheed is collecting data about cars in a car park.

Draw a line from each variable on the left to the type of data it is.

Rob wants to find out what students and staff think about the parking at his college.

The table shows information about the students and staff.

Rob decides to take a stratified sample of 80 from these groups of students and staff.

Work out the number of male students aged 19+ that should be in the sample

Ismail records the animals he sees on a safari.

Which word does not describe the type of data he collects?

James and Kia are doing a survey about how people travel to work.

James asks 10 people at a bus stop one morning.

Kia asks 40 people, chosen at random, in the town centre every day for a week.

Make two comparisons of their methods of collecting data.

Amy is also doing a survey about travel.

She collects this information about how teachers travel to her school.

Amy wants to ask some of the teachers more questions about travel.

She decides to ask a sample of 30 of these teachers, stratified by type of transport.

Work out how many teachers she should ask from each group.

Car ____________________________________
Bus ____________________________________
Walk ___________________________________

Jenny is carrying out a survey about cars passing her school.

She records the colour of each car.

Tick(✓) the two words that describe the type of data she is collecting.

She records the year of registration of every 20th car that passes, starting with the first car that passes.

Explain why this is not a random sample.

There are 120 applicants for a new television show.

The table shows information about their ages.

Draw a histogram to represent this information.

The 120 applicants were all given a task to complete.

The histogram represents the times they took to complete the task.

Those applicants who completed the task in 18 minutes or less were selected for the show.

Estimate the number of applicants who were selected for the show.

The television manager wants to interview some of the applicants about their experience of doing the task.

Here is some more information about the applicants.

The manager wants a sample of 50 applicants, stratified by age group and gender.

How many females from the age group should he select?

A company runs 5 gyms in a city.

Each gym has 140 members.

The owner of the company wants to conduct a face-to-face survey among the members. She decides to use a cluster sample.

Is this a suitable sampling method to use?
Give reason for your answer.

For a different survey, the owner needs to consider the different genders of the 700 members.

There are 580 males and 120 females.

What type of sampling method should she use?

She requires a sample of 175 members.

How many more males than females should be in her sample?