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OCR GCSE Maths

Topic questions Statistics Outliers

Outliers

17 questions · 122 marks · about 2 hours

Outliers questions

TopicOutliers

OCR J560 Outliers 17 questions

Paper 1 November 2024 Foundation tier, Question 19, also on the Higher paper 8 marks

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.

Week12345678910
Price per litre (£)1.421.451.471.501.541.601.571.521.611.46
Litres sold per day740725620705685660675695655715

The results for the first nine weeks are plotted on the scatter diagram.

Figure for question 19
(a)

Plot the result for week 10.

[1]
Reveal mark scheme Mark scheme for question 19(a)
(b)

Describe the type of correlation shown in the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 19(b)
(c)

In one week, there was a delay with petrol deliveries.

Circle the most likely point on the scatter diagram for that week.

[1]
Reveal mark scheme Mark scheme for question 19(c)
(d)(i)

On the scatter diagram, draw a line of best fit.

[1]
Reveal mark scheme Mark scheme for question 19(d)(i)
(d)(ii)

Use the line of best fit to estimate the average daily sales when the price per litre of petrol is £1.48.

[1]
Reveal mark scheme Mark scheme for question 19(d)(ii)
(e)

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.

[3]
Reveal mark scheme Mark scheme for question 19(e)

Paper 4 November 2024 Higher tier, Question 4, also on the Foundation paper 8 marks

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.

Week12345678910
Price per litre (£)1.421.451.471.501.541.601.571.521.611.46
Litres sold per day740725620705685660675695655715

The results for the first nine weeks are plotted on the scatter diagram.

Figure for question 4
(a)

Plot the result for week 10.

[1]
Reveal mark scheme Mark scheme for question 4(a)
(b)

Describe the type of correlation shown in the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 4(b)
(c)

In one week, there was a delay with petrol deliveries.

Circle the most likely point on the scatter diagram for that week.

[1]
Reveal mark scheme Mark scheme for question 4(c)
(d)(i)

On the scatter diagram, draw a line of best fit.

[1]
Reveal mark scheme Mark scheme for question 4(d)(i)
(d)(ii)

Use the line of best fit to estimate the average daily sales when the price per litre of petrol is £1.48.

[1]
Reveal mark scheme Mark scheme for question 4(d)(ii)
(e)

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.

[3]
Reveal mark scheme Mark scheme for question 4(e)

Paper 2 June 2024 Foundation tier, Question 22, also on the Higher paper 8 marks

The scatter diagram shows the test scores for 20 pupils in Science and Mathematics.

Figure for question 22
(a)

Describe the type of correlation shown in the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 22(a)
(b)

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.

[1]
Reveal mark scheme Mark scheme for question 22(b)
(c)

By drawing a line of best fit, estimate the test score in Mathematics for a pupil who scored 28 in the Science test.

[2]
Reveal mark scheme Mark scheme for question 22(c)
(d)

Explain why using the scatter diagram to estimate the test score in Mathematics for a pupil who scored 60 in Science may be unreliable.

[1]
Reveal mark scheme Mark scheme for question 22(d)
(e)

Find the percentage of the 20 pupils who scored less than 30 marks in both Science and Mathematics.

[3]
Reveal mark scheme Mark scheme for question 22(e)

Paper 5 June 2024 Higher tier, Question 4, also on the Foundation paper 8 marks

The scatter diagram shows the test scores for 20 pupils in Science and Mathematics.

Figure for question 4
(a)

Describe the type of correlation shown in the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 4(a)
(b)

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.

[1]
Reveal mark scheme Mark scheme for question 4(b)
(c)

By drawing a line of best fit, estimate the test score in Mathematics for a pupil who scored 28 in the Science test.

[2]
Reveal mark scheme Mark scheme for question 4(c)
(d)

Explain why using the scatter diagram to estimate the test score in Mathematics for a pupil who scored 60 in Science may be unreliable.

[1]
Reveal mark scheme Mark scheme for question 4(d)
(e)

Find the percentage of the 20 pupils who scored less than 30 marks in both Science and Mathematics.

[3]
Reveal mark scheme Mark scheme for question 4(e)

Paper 3 November 2023 Foundation tier, Question 19, also on the Higher paper 7 marks

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.

Figure for question 19
(a)(i)

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.

[1]
Reveal mark scheme Mark scheme for question 19(a)(i)
(a)(ii)

Describe the type of correlation shown on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 19(a)(ii)
(b)

One of Beth’s jigsaw puzzles was described as “the most difficult jigsaw puzzle you will ever try”.

(b)(i)

Circle the most likely jigsaw puzzle on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 19(b)(i)
(b)(ii)

Give a reason why you chose this jigsaw puzzle.

[1]
Reveal mark scheme Mark scheme for question 19(b)(ii)
(c)(i)

Draw a line of best fit on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 19(c)(i)
(c)(ii)

Use your line of best fit to estimate how many pieces are in a jigsaw puzzle that takes Beth 500 minutes to complete.

[1]
Reveal mark scheme Mark scheme for question 19(c)(ii)
(d)

Explain why Beth should not use her scatter diagram to estimate how long it will take to complete a jigsaw puzzle containing 8000 pieces.

[1]
Reveal mark scheme Mark scheme for question 19(d)

Paper 6 November 2023 Higher tier, Question 1, also on the Foundation paper 7 marks

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.

Figure for question 1
(a)(i)

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.

[1]
Reveal mark scheme Mark scheme for question 1(a)(i)
(a)(ii)

Describe the type of correlation shown on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 1(a)(ii)
(b)

One of Beth’s jigsaw puzzles was described as “the most difficult jigsaw puzzle you will ever try”.

(b)(i)

Circle the most likely jigsaw puzzle on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 1(b)(i)
(b)(ii)

Give a reason why you chose this jigsaw puzzle.

[1]
Reveal mark scheme Mark scheme for question 1(b)(ii)
(c)(i)

Draw a line of best fit on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 1(c)(i)
(c)(ii)

Use your line of best fit to estimate how many pieces are in a jigsaw puzzle that takes Beth 500 minutes to complete.

[1]
Reveal mark scheme Mark scheme for question 1(c)(ii)
(d)

Explain why Beth should not use her scatter diagram to estimate how long it will take to complete a jigsaw puzzle containing 8000 pieces.

[1]
Reveal mark scheme Mark scheme for question 1(d)

Paper 2 June 2023 Foundation tier, Question 21, also on the Higher paper 8 marks

The table shows the ages and heights of 12 children.

Age (years)241261011131157914
Height (m)0.841.011.51.41.41.351.621.421.141.241.261.68

The points for the first eight children (shaded in the table above) are plotted on the scatter diagram.

Figure for question 21
(a)

Plot the points for the remaining four children.

[2]
Reveal mark scheme Mark scheme for question 21(a)
(b)

Describe the type of correlation shown in the completed scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 21(b)
(c)

One of these children is taller than expected for their age.

On the scatter diagram, circle the point representing this child.

[1]
Reveal mark scheme Mark scheme for question 21(c)
(d)(i)

Kai is 8 years old. By drawing a line of best fit, estimate Kai’s height.

[2]
Reveal mark scheme Mark scheme for question 21(d)(i)
(d)(ii)

Describe an assumption you have made in giving your answer to part (d)(i).

[1]
Reveal mark scheme Mark scheme for question 21(d)(ii)
(e)

Explain why using this data to estimate the height of a child that is 17 years old may be unreliable.

[1]
Reveal mark scheme Mark scheme for question 21(e)

Paper 5 June 2023 Higher tier, Question 5, also on the Foundation paper 8 marks

The table shows the ages and heights of 12 children.

Age (years)241261011131157914
Height (m)0.841.011.51.41.41.351.621.421.141.241.261.68

The points for the first eight children (shaded in the table above) are plotted on the scatter diagram.

Figure for question 5
(a)

Plot the points for the remaining four children.

[2]
Reveal mark scheme Mark scheme for question 5(a)
(b)

Describe the type of correlation shown in the completed scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 5(b)
(c)

One of these children is taller than expected for their age.

On the scatter diagram, circle the point representing this child.

[1]
Reveal mark scheme Mark scheme for question 5(c)
(d)(i)

Kai is 8 years old. By drawing a line of best fit, estimate Kai’s height.

[2]
Reveal mark scheme Mark scheme for question 5(d)(i)
(d)(ii)

Describe an assumption you have made in giving your answer to part (d)(i).

[1]
Reveal mark scheme Mark scheme for question 5(d)(ii)
(e)

Explain why using this data to estimate the height of a child that is 17 years old may be unreliable.

[1]
Reveal mark scheme Mark scheme for question 5(e)

Paper 3 November 2022 Foundation tier, Question 24, also on the Higher paper 5 marks

The scatter diagram shows the number of visitors to a children’s playground and the maximum temperature on fifteen Saturdays in summer.

Figure for question 24
(a)

Describe the type of correlation shown in the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 24(a)
(b)

One Saturday was a hot but stormy day.

(b)(i)

Circle the most likely point on the scatter diagram for this Saturday.

[1]
Reveal mark scheme Mark scheme for question 24(b)(i)
(b)(ii)

Explain why you chose this point.

[1]
Reveal mark scheme Mark scheme for question 24(b)(ii)
(c)

Use a line of best fit to predict the number of visitors on a Saturday that has a maximum temperature of 21 °C.

[2]
Reveal mark scheme Mark scheme for question 24(c)

Paper 6 November 2022 Higher tier, Question 6, also on the Foundation paper 5 marks

The scatter diagram shows the number of visitors to a children’s playground and the maximum temperature on fifteen Saturdays in summer.

Figure for question 6
(a)

Describe the type of correlation shown in the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 6(a)
(b)

One Saturday was a hot but stormy day.

(b)(i)

Circle the most likely point on the scatter diagram for this Saturday.

[1]
Reveal mark scheme Mark scheme for question 6(b)(i)
(b)(ii)

Explain why you chose this point.

[1]
Reveal mark scheme Mark scheme for question 6(b)(ii)
(c)

Use a line of best fit to predict the number of visitors on a Saturday that has a maximum temperature of 21 °C.

[2]
Reveal mark scheme Mark scheme for question 6(c)

Paper 1 June 2022 Foundation tier, Question 21, also on the Higher paper 10 marks

The scatter diagram shows the midday temperature at 13 different heights on a mountain.

Figure for question 21
Question 21, shown as an image
(a)

The table has the information for 2 more heights.

Plot these on the scatter diagram.

Height (m)5001580
Temperature (°C)8.81.2
[2]
Reveal mark scheme Mark scheme for question 21(a)
(b)

Describe the type of correlation shown in the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 21(b)
(c)

By drawing a line of best fit, estimate the temperature at 1000 m.

[2]
Reveal mark scheme Mark scheme for question 21(c)
(d)

Circle the outlier on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 21(d)
(e)

Explain why using the scatter diagram to estimate the temperature at 1800 m may be unreliable.

[1]
Reveal mark scheme Mark scheme for question 21(e)
(f)

Find the percentage of the 15 temperatures which are below 6 °C.

[3]
Reveal mark scheme Mark scheme for question 21(f)

Paper 4 June 2022 Higher tier, Question 5, also on the Foundation paper 10 marks

The scatter diagram shows the midday temperature at 13 different heights on a mountain.

Figure for question 5
(a)

The table has the information for 2 more heights.

Plot these on the scatter diagram.

Height (m)5001580
Temperature (°C)8.81.2
[2]
Reveal mark scheme Mark scheme for question 5(a)
(b)

Describe the type of correlation shown in the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 5(b)
(c)

By drawing a line of best fit, estimate the temperature at 1000 m.

[2]
Reveal mark scheme Mark scheme for question 5(c)
(d)

Circle the outlier on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 5(d)
(e)

Explain why using the scatter diagram to estimate the temperature at 1800 m may be unreliable.

[1]
Reveal mark scheme Mark scheme for question 5(e)
(f)

Find the percentage of the 15 temperatures which are below 6 °C.

[3]
Reveal mark scheme Mark scheme for question 5(f)

Paper 3 November 2020 Foundation tier, Question 14, also on the Higher paper 6 marks

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.

Figure for question 14
(a)

The data for the final two flights is:

Duration210 minutes1 hour 40 minutes
Cost£130£80

Plot these flights on the scatter diagram.

[2]
Reveal mark scheme Mark scheme for question 14(a)
(b)

The cost of one of the 15 flights had been discounted in a sale.

Circle the most likely flight on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 14(b)
(c)(i)

Draw a line of best fit on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 14(c)(i)
(c)(ii)

Use your line of best fit to estimate the duration of a flight costing £90.

(c)(ii)........ minutes

[1]
Reveal mark scheme Mark scheme for question 14(c)(ii)
(d)

Explain why the travel agent should not use his records to estimate the cost of a 7 hour flight.

[1]
Reveal mark scheme Mark scheme for question 14(d)

Paper 6 November 2020 Higher tier, Question 1, also on the Foundation paper 6 marks

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.

Figure for question 1
(a)

The data for the final two flights is:

Duration210 minutes1 hour 40 minutes
Cost£130£80

Plot these flights on the scatter diagram.

[2]
Reveal mark scheme Mark scheme for question 1(a)
(b)

The cost of one of the 15 flights had been discounted in a sale.

Circle the most likely flight on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 1(b)
(c)(i)

Draw a line of best fit on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 1(c)(i)
(c)(ii)

Use your line of best fit to estimate the duration of a flight costing £90.

(c)(ii)........ minutes

[1]
Reveal mark scheme Mark scheme for question 1(c)(ii)
(d)

Explain why the travel agent should not use his records to estimate the cost of a 7 hour flight.

[1]
Reveal mark scheme Mark scheme for question 1(d)

Paper 5 June 2019 Higher tier, Question 5 8 marks

The table shows the ages and values of 11 cars of the same model.

Age (years)47111910437812
Value (thousands of pounds)9.26.01.211.42.34.23.48.05.65.00.4

The points for the first 7 cars are plotted on the scatter diagram.

Figure for question 5
(a)

Plot the points for the remaining 4 cars.

[2]
Reveal mark scheme Mark scheme for question 5(a)
(b)

Describe the type and strength of the correlation shown in the completed scatter diagram.

[2]
Reveal mark scheme Mark scheme for question 5(b)
(c)

One car lost its value more quickly than the other cars.

On the scatter diagram, draw a circle around the point representing this car.

[1]
Reveal mark scheme Mark scheme for question 5(c)
(d)

By drawing a line of best fit, estimate the value of a car that is 6 years old.

[2]
Reveal mark scheme Mark scheme for question 5(d)
(e)

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.

[1]
Reveal mark scheme Mark scheme for question 5(e)

Paper 3 June 2017 Foundation tier, Question 16, also on the Higher paper 5 marks

(a)

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.

Figure for question 16
(a)(i)

Circle the outlier on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 16(a)(i)
(a)(ii)

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.

[2]
Reveal mark scheme Mark scheme for question 16(a)(ii)
(a)(iii)

Explain why the scatter diagram should not be used to estimate the number of visitors on a day with 9 mm of rainfall.

[1]
Reveal mark scheme Mark scheme for question 16(a)(iii)
(b)

The pie chart summarises information about the visitors to the tourist attraction on a different

Figure for question 16

Explain why the pie chart cannot be used to work out how many adults visited on that day.

[1]
Reveal mark scheme Mark scheme for question 16(b)

Paper 6 June 2017 Higher tier, Question 3, also on the Foundation paper 5 marks

(a)

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.

Figure for question 3
(a)(i)

Circle the outlier on the scatter diagram.

[1]
Reveal mark scheme Mark scheme for question 3(a)(i)
(a)(ii)

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.

[2]
Reveal mark scheme Mark scheme for question 3(a)(ii)
(a)(iii)

Explain why the scatter diagram should not be used to estimate the number of visitors on a day with 9 mm of rainfall.

[1]
Reveal mark scheme Mark scheme for question 3(a)(iii)
(b)

The pie chart summarises information about the visitors to the tourist attraction on a different

Figure for question 3

Explain why the pie chart cannot be used to work out how many adults visited on that day.

[1]
Reveal mark scheme Mark scheme for question 3(b)

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