OCR GCSE Maths
Topic questions Statistics Sampling and populations
15 questions · 72 marks · about 1 hour
Also involves Sampling methods
A town council are going to do a survey on how people travel to work or school and for how long they travel.
One day their interviewer stands outside the town railway station and chooses 20 people at random to form their sample.
Make three different criticisms or suggestions for improving the councilās method for selecting their sample.
A town council are going to do a survey on how people travel to work or school and for how long they travel.
One day their interviewer stands outside the town railway station and chooses 20 people at random to form their sample.
Make three different criticisms or suggestions for improving the councilās method for selecting their sample.
A machine makes bolts that should be 30.0 mm long, correct to 1 decimal place.
Jane checks the accuracy of the machine by taking a random sample of 10 of the bolts. Here are the lengths, in mm correct to 1 decimal place, of the bolts in Janeās sample.
29.5 29.1 30.0 30.0 30.2 30.0 30.0 30.0 30.5 30.0
The machine makes 2000 of these bolts that day.
Jane says
6 of the 10 bolts in the sample are of the correct length. That is 60%. Therefore, 1200 of the 2000 bolts will be of the correct length because that is 60%.
Give a reason why Janeās claim may be unreliable.
Also involves The four operations
At an adventure park, all children participate in three activities, choosing exactly one activity from each of three options.
| Option | Activity |
| 1 | football or golf |
| 2 | bowling or climbing |
| 3 | rafting or swimming or tennis |
On one Monday morning, 100 children visited the adventure park.
The frequency tree shows the number of children choosing some of the activities.
Option 1
Option 2
Option 3
........
Complete the frequency tree.
Which was the most popular activity out of rafting, swimming and tennis? Show how you decide.
One of the 100 children is picked at random.
Find the probability that this child chose bowling.
Alex says
45% of all children coming to the adventure park choose football.
What assumption has Alex made?
A teacher is planning a theme day for the 500 pupils at their school. The teacher asks a sample of 20 pupils from year 8 which theme they would prefer.
The results are shown in the table.
| Theme | Number of pupils |
| Sport | 7 |
| Art and design | 3 |
| Recipes | 2 |
| Music and movies | 8 |
Describe two disadvantages of the teacherās sampling method.
Using the results from the table, the teacher estimates that 175 pupils in the school would prefer a sport theme.
Here is the teacherās method.
Write down one assumption the teacher has made when making their estimate.
A teacher is planning a theme day for the 500 pupils at their school. The teacher asks a sample of 20 pupils from year 8 which theme they would prefer.
The results are shown in the table.
| Theme | Number of pupils |
| Sport | 7 |
| Art and design | 3 |
| Recipes | 2 |
| Music and movies | 8 |
Describe two disadvantages of the teacherās sampling method.
Using the results from the table the teacher estimates that 175 pupils in the school would prefer a sport theme.
Here is the teacherās method.
Write down one assumption the teacher has made when making their estimate.
A student is researching the difference in how much exercise adults and children do. To collect their data, the student interviews the first 25 people found in the High Street at 11 am on one Monday morning.
Make three different criticisms of the studentās method of collecting data.
Here is the data collection table that the student used.
Make one criticism of the studentās table.
Also involves Sampling methods
A journalist is going to do a survey to find out whether people aged 15 or less spend more time playing computer games than people aged more than 15.
The journalist says their sample will be the first 20 people leaving a particular shop after 9 am next Monday.
Give one reason why the journalistās sample is unlikely to give reliable information.
Make three suggestions to help the journalist obtain a sample that may give more reliable information.
Also involves Box plots and stem and leaf diagrams
The box plot shows the distribution of the lengths, in cm, of 60 full-grown mice owned by a pet
Find the range.
Work out the number of these mice that have a length of at least 7.2 cm.
Sam owns 5 full-grown mice. Sam picks the third longest mouse and measures its length. Sam then looks at the box plot.
Sam says
This mouse is 7.35 cm long. Therefore, the mice I own are longer than the full-grown mice owned by the pet shop.
Give a mathematical reason to support Samās conclusion.
Give a mathematical reason why Samās conclusion may be unreliable.
Lee wishes to find out if there is a relationship between a personās age and the time it takes them to complete a puzzle.
Lee decides to conduct an experiment. She asks 12 people to complete the puzzle. She records each personās age and the time taken to complete the puzzle.
Make one criticism of Leeās method.
This scatter diagram shows the results for ten of the people in Leeās experiment.
Here are the other two results.
| Age (years) | 47 | 60 |
| Time (seconds) | 21 | 34 |
Plot these results on the scatter diagram.
What type of correlation is shown in the scatter diagram?
Estimate the time it would take a person aged 35 to complete the puzzle. Show your working to justify your answer.
Lee says that at least 80% of the 12 people completed the puzzle in under 30 seconds.
Is Lee correct? Show working to support your answer.
Also involves Percentages
Lee wishes to find out if there is a relationship between a personās age and the time it takes them to complete a puzzle.
Lee decides to conduct an experiment. She asks 12 people to complete the puzzle. She records each personās age and the time taken to complete the puzzle.
Make one criticism of Leeās method.
This scatter diagram shows the results for ten of the people in Leeās experiment.
Here are the other two results.
| Age (years) | 47 | 60 |
| Time (seconds) | 21 | 34 |
Plot these results on the scatter diagram.
What type of correlation is shown in the scatter diagram?
Estimate the time it would take a person aged 35 to complete the puzzle.
Show your working to justify your answer.
Lee says that at least 80% of the 12 people completed the puzzle in under 30 seconds.
Is Lee correct? Show working to support your answer.
Ceri records the time taken, t minutes, to travel to school for a sample of 168 students at her
Draw a histogram to represent this information.
Ceri says
The longest time that any of these students took to travel to school was 80 minutes.
Is she correct? Give a reason for your answer.
Ceri also claims that 25% of all of the students at this Academy took more than 30 minutes to travel to school.
Show how Ceri might have worked out her claim.
State one assumption that Ceri has made in making her claim.
Jack carries out a survey in his school. He selects 50 students, at random, and asks them
Do you think that it is a good idea to have women-only railway carriages?
These are his results.
| Number of students | |
| Yes | 32 |
| No | 13 |
| Donāt know | 5 |
What percentage of the students in Jackās survey answered āYesā?
Jack says
My survey shows that people in England think that it is a good idea to have women-only railway carriages.
Explain why Jack may be wrong.
George is the manager of a shoe shop. He samples 50 of his customers and asks them about the one style of shoe they would buy next. The table shows his results.
| Style of shoe | Number of customers |
| Laced shoes | 18 |
| Boots | 15 |
| Sandals | 8 |
| Trainers | 5 |
| Other | 4 |
George buys 1000 pairs of shoes with the number of each style based on his survey results.
How many pairs of sandals should he buy? Write down any assumption you make about his sample.
George is the manager of a shoe shop. He samples 50 of his customers and asks them about the one style of shoe they would buy next. The table shows his results.
| Style of shoe | Number of customers |
| Laced shoes | 18 |
| Boots | 15 |
| Sandals | 8 |
| Trainers | 5 |
| Other | 4 |
George buys 1000 pairs of shoes with the number of each style based on his survey results.
How many pairs of sandals should he buy? Write down any assumption you make about his sample.
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