OCR GCSE Maths
Topic questions Statistics Scatter diagrams
35 questions · 240 marks · about 3.5 hours
Describe the correlation shown in each of these scatter diagrams.
A theatre records the number of seats sold and the profit made for 10 performances. The scatter diagram shows these results.
By drawing a line of best fit, estimate the profit made when 250 seats are sold.
Describe the correlation shown in each of these scatter diagrams.
A theatre records the number of seats sold and the profit made for 10 performances. The scatter diagram shows these results.
By drawing a line of best fit, estimate the profit made when 250 seats are sold.
Also involves Using a calculator
Each week the manager of a petrol station records the average daily sales, in litres, and the average price, in pounds, of a litre of petrol for that week.
The table shows their results for ten weeks.
| Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Price per litre (£) | 1.42 | 1.45 | 1.47 | 1.50 | 1.54 | 1.60 | 1.57 | 1.52 | 1.61 | 1.46 |
| Litres sold per day | 740 | 725 | 620 | 705 | 685 | 660 | 675 | 695 | 655 | 715 |
The results for the first nine weeks are plotted on the scatter diagram.
Plot the result for week 10.
Describe the type of correlation shown in the scatter diagram.
In one week, there was a delay with petrol deliveries.
Circle the most likely point on the scatter diagram for that week.
On the scatter diagram, draw a line of best fit.
Use the line of best fit to estimate the average daily sales when the price per litre of petrol is £1.48.
The manager says,
As the sales go down, the total amount of money we take stays roughly the same.
Find evidence to support this statement.
Also involves The four operations
Each week the manager of a petrol station records the average daily sales, in litres, and the average price, in pounds, of a litre of petrol for that week.
The table shows their results for ten weeks.
| Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Price per litre (£) | 1.42 | 1.45 | 1.47 | 1.50 | 1.54 | 1.60 | 1.57 | 1.52 | 1.61 | 1.46 |
| Litres sold per day | 740 | 725 | 620 | 705 | 685 | 660 | 675 | 695 | 655 | 715 |
The results for the first nine weeks are plotted on the scatter diagram.
Plot the result for week 10.
Describe the type of correlation shown in the scatter diagram.
In one week, there was a delay with petrol deliveries.
Circle the most likely point on the scatter diagram for that week.
On the scatter diagram, draw a line of best fit.
Use the line of best fit to estimate the average daily sales when the price per litre of petrol is £1.48.
The manager says,
As the sales go down, the total amount of money we take stays roughly the same.
Find evidence to support this statement.
The scatter diagram shows the test scores for 20 pupils in Science and Mathematics.
Describe the type of correlation shown in the scatter diagram.
One pupil took the Science test but was then ill during the Mathematics test and had to leave early.
On the scatter diagram, circle the point that is most likely to represent this pupil.
By drawing a line of best fit, estimate the test score in Mathematics for a pupil who scored 28 in the Science test.
Explain why using the scatter diagram to estimate the test score in Mathematics for a pupil who scored 60 in Science may be unreliable.
Find the percentage of the 20 pupils who scored less than 30 marks in both Science and Mathematics.
The scatter diagram shows the test scores for 20 pupils in Science and Mathematics.
Describe the type of correlation shown in the scatter diagram.
One pupil took the Science test but was then ill during the Mathematics test and had to leave early.
On the scatter diagram, circle the point that is most likely to represent this pupil.
By drawing a line of best fit, estimate the test score in Mathematics for a pupil who scored 28 in the Science test.
Explain why using the scatter diagram to estimate the test score in Mathematics for a pupil who scored 60 in Science may be unreliable.
Find the percentage of the 20 pupils who scored less than 30 marks in both Science and Mathematics.
Beth completes some jigsaw puzzles and records the following information.
• The number of pieces in the jigsaw puzzle.
• The time taken to complete the jigsaw puzzle, in minutes.
Beth shows this information in a scatter diagram.
Beth completes two more jigsaw puzzles.
• A 3000 piece jigsaw puzzle taking 460 minutes.
• A 1300 piece jigsaw puzzle taking 320 minutes.
Show this information on the scatter diagram.
Describe the type of correlation shown on the scatter diagram.
One of Beth’s jigsaw puzzles was described as “the most difficult jigsaw puzzle you will ever try”.
Circle the most likely jigsaw puzzle on the scatter diagram.
Give a reason why you chose this jigsaw puzzle.
Draw a line of best fit on the scatter diagram.
Use your line of best fit to estimate how many pieces are in a jigsaw puzzle that takes Beth 500 minutes to complete.
Explain why Beth should not use her scatter diagram to estimate how long it will take to complete a jigsaw puzzle containing 8000 pieces.
The graph shows the value of sunscreen products sold in a shop for each quarter from quarter 1 of 2021 to quarter 4 of 2023.
| 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 |
| 2021 | 2022 | 2023 |
Year and quarter
Make one comment about the annual variation shown in this graph.
In one of these years, quarter 3 was very cloudy. Write down which year this is most likely to be. Give a reason for your answer.
The manager of the shop says that the value of sales in quarter 4 of 2024 will be £3100. What assumption has the manager made?
Beth completes some jigsaw puzzles and records the following information.
• The number of pieces in the jigsaw puzzle.
• The time taken to complete the jigsaw puzzle, in minutes.
Beth shows this information in a scatter diagram.
Beth completes two more jigsaw puzzles.
• A 3000 piece jigsaw puzzle taking 460 minutes.
• A 1300 piece jigsaw puzzle taking 320 minutes.
Show this information on the scatter diagram.
Describe the type of correlation shown on the scatter diagram.
One of Beth’s jigsaw puzzles was described as “the most difficult jigsaw puzzle you will ever try”.
Circle the most likely jigsaw puzzle on the scatter diagram.
Give a reason why you chose this jigsaw puzzle.
Draw a line of best fit on the scatter diagram.
Use your line of best fit to estimate how many pieces are in a jigsaw puzzle that takes Beth 500 minutes to complete.
Explain why Beth should not use her scatter diagram to estimate how long it will take to complete a jigsaw puzzle containing 8000 pieces.
The table shows the ages and heights of 12 children.
| Age (years) | 2 | 4 | 12 | 6 | 10 | 11 | 13 | 11 | 5 | 7 | 9 | 14 |
| Height (m) | 0.84 | 1.01 | 1.5 | 1.4 | 1.4 | 1.35 | 1.62 | 1.42 | 1.14 | 1.24 | 1.26 | 1.68 |
The points for the first eight children (shaded in the table above) are plotted on the scatter diagram.
Plot the points for the remaining four children.
Describe the type of correlation shown in the completed scatter diagram.
One of these children is taller than expected for their age.
On the scatter diagram, circle the point representing this child.
Kai is 8 years old. By drawing a line of best fit, estimate Kai’s height.
Describe an assumption you have made in giving your answer to part (d)(i).
Explain why using this data to estimate the height of a child that is 17 years old may be unreliable.
The table shows the ages and heights of 12 children.
| Age (years) | 2 | 4 | 12 | 6 | 10 | 11 | 13 | 11 | 5 | 7 | 9 | 14 |
| Height (m) | 0.84 | 1.01 | 1.5 | 1.4 | 1.4 | 1.35 | 1.62 | 1.42 | 1.14 | 1.24 | 1.26 | 1.68 |
The points for the first eight children (shaded in the table above) are plotted on the scatter diagram.
Plot the points for the remaining four children.
Describe the type of correlation shown in the completed scatter diagram.
One of these children is taller than expected for their age.
On the scatter diagram, circle the point representing this child.
Kai is 8 years old. By drawing a line of best fit, estimate Kai’s height.
Describe an assumption you have made in giving your answer to part (d)(i).
Explain why using this data to estimate the height of a child that is 17 years old may be unreliable.
Also involves The four operations
The graph shows information about the population of a village.
The population of the village in 2021 was 4740.
Plot this point on the graph.
Work out the increase in the population of the village between 2016 and 2018.
Rowan says that there was a huge increase in the population of the village between 2015 and 2020.
Describe how Rowan may have been misled by the graph.
Blake says that the population of the village will be greater than 4800 in 2022.
Write down an assumption Blake has made.
Also involves Real-life graphs
A ball of dough is left to rise before it is baked. The graph shows the height of the ball of dough over the first 20 minutes.
Work out the gradient of the line as a decimal, giving the units of your answer. Show how you work out your answer.
A baker works out the height of the ball of dough at the end of 25 minutes as 14 cm.
Use your gradient to show that the baker could be correct.
What assumption has the baker made?
The scatter diagram shows the number of visitors to a children’s playground and the maximum temperature on fifteen Saturdays in summer.
Describe the type of correlation shown in the scatter diagram.
One Saturday was a hot but stormy day.
Circle the most likely point on the scatter diagram for this Saturday.
Explain why you chose this point.
Use a line of best fit to predict the number of visitors on a Saturday that has a maximum temperature of 21 °C.
The scatter diagram shows the number of visitors to a children’s playground and the maximum temperature on fifteen Saturdays in summer.
Describe the type of correlation shown in the scatter diagram.
One Saturday was a hot but stormy day.
Circle the most likely point on the scatter diagram for this Saturday.
Explain why you chose this point.
Use a line of best fit to predict the number of visitors on a Saturday that has a maximum temperature of 21 °C.
The scatter diagram shows the midday temperature at 13 different heights on a mountain.
The table has the information for 2 more heights.
Plot these on the scatter diagram.
| Height (m) | 500 | 1580 |
| Temperature (°C) | 8.8 | 1.2 |
Describe the type of correlation shown in the scatter diagram.
By drawing a line of best fit, estimate the temperature at 1000 m.
Circle the outlier on the scatter diagram.
Explain why using the scatter diagram to estimate the temperature at 1800 m may be unreliable.
Find the percentage of the 15 temperatures which are below 6 °C.
The scatter diagram shows the midday temperature at 13 different heights on a mountain.
The table has the information for 2 more heights.
Plot these on the scatter diagram.
| Height (m) | 500 | 1580 |
| Temperature (°C) | 8.8 | 1.2 |
Describe the type of correlation shown in the scatter diagram.
By drawing a line of best fit, estimate the temperature at 1000 m.
Circle the outlier on the scatter diagram.
Explain why using the scatter diagram to estimate the temperature at 1800 m may be unreliable.
Find the percentage of the 15 temperatures which are below 6 °C.
The table shows the marks obtained by 10 students in spelling tests in January and February.
| Mark in January | 26 | 53 | 50 | 48 | 30 | 66 | 70 | 44 | 37 | 38 |
| Mark in February | 42 | 58 | 68 | 58 | 66 | 82 | 86 | 60 | 48 | 50 |
The marks for the first six students are plotted on the scatter diagram.
Plot the marks for the remaining four students.
Describe the type of correlation shown in the completed scatter diagram.
On the scatter diagram, circle the student that made the greatest improvement in their
marks from January to February.
Work out the percentage change in this student’s marks from January to February.
Another student, Kai, scored 79 marks in the test in January but was absent for the test in February.
Kai says
I could use a line of best fit on the scatter diagram to estimate the marks I may have achieved in the test in February.
Is Kai’s method reliable? Give a reason for your answer.
The table shows the marks obtained by 10 students in spelling tests in January and February.
| Mark in January | 26 | 53 | 50 | 48 | 30 | 66 | 70 | 44 | 37 | 38 |
| Mark in February | 42 | 58 | 68 | 58 | 66 | 82 | 86 | 60 | 48 | 50 |
The marks for the first six students are plotted on the scatter diagram.
Plot the marks for the remaining four students.
Describe the type of correlation shown in the completed scatter diagram.
On the scatter diagram, circle the student that made the greatest improvement in their
marks from January to February.
Work out the percentage change in this student’s marks from January to February.
Another student, Kai, scored 79 marks in the test in January but was absent for the test in February.
Kai says
I could use a line of best fit on the scatter diagram to estimate the marks I may have achieved in the test in February.
Is Kai’s method reliable? Give a reason for your answer.
A travel agent records the duration and cost of the 15 flights he sold on one day. The data for the first 13 flights are plotted on the scatter diagram.
The data for the final two flights is:
| Duration | 210 minutes | 1 hour 40 minutes |
| Cost | £130 | £80 |
Plot these flights on the scatter diagram.
The cost of one of the 15 flights had been discounted in a sale.
Circle the most likely flight on the scatter diagram.
Draw a line of best fit on the scatter diagram.
Use your line of best fit to estimate the duration of a flight costing £90.
(c)(ii)........ minutes
Explain why the travel agent should not use his records to estimate the cost of a 7 hour flight.
A travel agent records the duration and cost of the 15 flights he sold on one day. The data for the first 13 flights are plotted on the scatter diagram.
The data for the final two flights is:
| Duration | 210 minutes | 1 hour 40 minutes |
| Cost | £130 | £80 |
Plot these flights on the scatter diagram.
The cost of one of the 15 flights had been discounted in a sale.
Circle the most likely flight on the scatter diagram.
Draw a line of best fit on the scatter diagram.
Use your line of best fit to estimate the duration of a flight costing £90.
(c)(ii)........ minutes
Explain why the travel agent should not use his records to estimate the cost of a 7 hour flight.
12 students take two tests. Each test is out of 60. The scatter diagram shows the results for 10 of the students.
The table shows the results for the other 2 students.
| Test 1 | 36 | 38 |
| Test 2 | 44 | 41 |
Plot these results on the scatter diagram.
Describe the type of correlation shown in the scatter diagram.
Draw a line of best fit on the scatter diagram.
Another student was absent for Test 2. The student scored 40 marks on Test 1.
Use your line of best fit to estimate a result for this student on Test 2.
Work out the percentage of the 12 students whose result on Test 1 is lower than their result on Test 2.
12 students take two tests. Each test is out of 60. The scatter diagram shows the results for 10 of the students.
The table shows the results for the other 2 students.
| Test 1 | 36 | 38 |
| Test 2 | 44 | 41 |
Plot these results on the scatter diagram.
Describe the type of correlation shown in the scatter diagram.
Draw a line of best fit on the scatter diagram.
Another student was absent for Test 2. The student scored 40 marks on Test 1.
Use your line of best fit to estimate a result for this student on Test 2.
Work out the percentage of the 12 students whose result on Test 1 is lower than their result on Test 2.
A doctor records the ages, in years, and the heights, in centimetres, of 10 girls.
| Age (years) | 2 | 5 | 3 | 7 | 5 | 8 | 3 | 6 | 9 | 4 |
| Height (cm) | 85 | 115 | 93 | 120 | 110 | 125 | 90 | 117 | 127 | 103 |
The points for the first six girls are plotted on the scatter diagram.
Plot the points for the remaining four girls.
Describe the type of correlation shown in the scatter diagram.
The doctor says that by using a line of best fit on the scatter diagram, the height of a 6‑year‑old girl is around 95 cm.
Does the scatter diagram support the doctor’s statement? Explain your reasoning.
Explain why the scatter diagram and line of best fit should not be used to estimate the height of a 12‑year‑old girl.
The table shows the ages and values of 11 cars of the same model.
| Age (years) | 4 | 7 | 11 | 1 | 9 | 10 | 4 | 3 | 7 | 8 | 12 |
| Value (thousands of pounds) | 9.2 | 6.0 | 1.2 | 11.4 | 2.3 | 4.2 | 3.4 | 8.0 | 5.6 | 5.0 | 0.4 |
The points for the first 7 cars are plotted on the scatter diagram.
Plot the points for the remaining 4 cars.
Describe the type and strength of the correlation shown in the completed scatter diagram.
One car lost its value more quickly than the other cars.
On the scatter diagram, draw a circle around the point representing this car.
By drawing a line of best fit, estimate the value of a car that is 6 years old.
Explain the limitations of using the equation of the line of best fit to estimate the value of a car that is 16 years old.
Also involves The four operations
The table shows the number of computers sold in Tom’s shop each quarter from 2015 to 2017.
| 2015 | 2016 | 2017 | ||||||||||
| Quarter | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 |
| Number of computers sold | 13 | 31 | 29 | 45 | 20 | 32 | 25 | 47 | 27 | 40 | 30 | 58 |
Complete this graph using the information for 2017.
Tom adds the three results for quarter 1 and he adds the three results for quarter 4. Tom says
The ratio of the total number of computers sold in quarter 1 compared to quarter 4 is 2: 5.
Is he correct? Show your reasoning.
Make two comments about Tom’s sales over the period 2015 to 2017.
Tom predicts that he will sell more than 60 computers in the 4th quarter of 2018.
What assumption has he made?
In a dance competition, two judges each award scores out of 30. The scatter diagram shows the scores awarded to the first 10 dancers.
Here are the scores for the next two dancers.
| Judge A | 21 | 7 |
| Judge B | 18 | 8 |
Plot their scores on the scatter diagram.
Dancers who are awarded a score of more than 20 by both judges receive a medal.
For the 12 dancers, express the ratio of medal winners to non-medal winners in its simplest form.
This chart shows the types of dance performed by the 12 dancers.
3 performed a street dance, 8 performed a jazz dance and 1 performed a tap dance.
Why is this diagram misleading?
Also involves The four operations
The table shows the number of computers sold in Tom’s shop each quarter from 2015 to 2017.
| 2015 | 2016 | 2017 | ||||||||||
| Quarter | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 |
| Number of computers sold | 13 | 31 | 29 | 45 | 20 | 32 | 25 | 47 | 27 | 40 | 30 | 58 |
Complete this graph using the information for 2017.
Tom adds the three results for quarter 1 and he adds the three results for quarter 4. Tom says
The ratio of the total number of computers sold in quarter 1 compared to quarter 4 is 2: 5.
Is he correct? Show your reasoning.
Make two comments about Tom’s sales over the period 2015 to 2017.
Tom predicts that he will sell more than 60 computers in the 4th quarter of 2018.
What assumption has he made?
In a dance competition, two judges each award scores out of 30. The scatter diagram shows the scores awarded to the first 10 dancers.
Here are the scores for the next two dancers.
| Judge A | 21 | 7 |
| Judge B | 18 | 8 |
Plot their scores on the scatter diagram.
Dancers who are awarded a score of more than 20 by both judges receive a medal.
For the 12 dancers, express the ratio of medal winners to non-medal winners in its simplest form.
This chart shows the types of dance performed by the 12 dancers.
3 performed a street dance, 8 performed a jazz dance and 1 performed a tap dance.
Why is this diagram misleading?
Lee wishes to find out if there is a relationship between a person’s 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 person’s age and the time taken to complete the puzzle.
Make one criticism of Lee’s method.
This scatter diagram shows the results for ten of the people in Lee’s 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 person’s 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 person’s age and the time taken to complete the puzzle.
Make one criticism of Lee’s method.
This scatter diagram shows the results for ten of the people in Lee’s 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.
The scatter diagram shows the results of 17 students in their French test and their German test. Both tests are out of 100.
Here are the results of another 4 students.
| French | 21 | 75 | 48 | 53 |
| German | 30 | 78 | 46 | 61 |
Plot these results on the scatter diagram.
Describe the type and strength of the correlation shown in this diagram.
Work out the percentage of the students whose German result was higher than their French result.
The scatter diagram shows the results of 17 students in their French test and their German test. Both tests are out of 100.
Here are the results of another 4 students.
| French | 21 | 75 | 48 | 53 |
| German | 30 | 78 | 46 | 61 |
Plot these results on the scatter diagram.
Describe the type and strength of the correlation shown in this diagram.
Work out the percentage of the students whose German result was higher than their French result.
The owner of a tourist attraction records the amount of rainfall, in millimetres, and the number of visitors each day. The results for 10 days are shown in the scatter diagram.
Circle the outlier on the scatter diagram.
The owner claims that he would expect around 320 visitors on a day with 2 mm of rainfall.
Does the scatter diagram support his statement? Explain how you made your decision.
Explain why the scatter diagram should not be used to estimate the number of visitors on a day with 9 mm of rainfall.
The pie chart summarises information about the visitors to the tourist attraction on a different
Explain why the pie chart cannot be used to work out how many adults visited on that day.
The owner of a tourist attraction records the amount of rainfall, in millimetres, and the number of visitors each day. The results for 10 days are shown in the scatter diagram.
Circle the outlier on the scatter diagram.
The owner claims that he would expect around 320 visitors on a day with 2 mm of rainfall.
Does the scatter diagram support his statement? Explain how you made your decision.
Explain why the scatter diagram should not be used to estimate the number of visitors on a day with 9 mm of rainfall.
The pie chart summarises information about the visitors to the tourist attraction on a different
Explain why the pie chart cannot be used to work out how many adults visited on that day.
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