Scatter Graphs & Correlation (Cambridge International IGCSE Mathematics): Exam Questions

Ten athletes compete in both the 100 metre race and the triple jump. Their results are shown in the scatter diagram.

One of these athletes jumps 15.12m in the triple jump.

Write down his time for the 100 metre race.

.................................................. s

Extract:

Ten athletes compete in both the 100 metre race and the triple jump. Their results are shown in the scatter diagram.

The values for two other athletes are shown in the table.

On the scatter diagram, plot these points.

Extract:

Ten athletes compete in both the 100 metre race and the triple jump. Their results are shown in the scatter diagram. One of these athletes jumps 15.12m in the triple jump. Write down his time for the 100 metre race. The values for two other athletes are shown in the table. | Distance in the triple jump (m) | 14.74 | 15.2 | | Time for 100m (seconds) | 13.2 | 12.76 | On the scatter diagram, plot these points.

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

Extract:

Ten athletes compete in both the 100 metre race and the triple jump. Their results are shown in the scatter diagram.

What type of correlation is shown in the scatter diagram?

Write down the type of correlation you would expect for the following.

The average speed of a train and the time taken for a journey.

The distance travelled by a car and the amount of fuel used.

“We eat more ice cream as the temperature rises.”

What type of correlation is this?

A teacher gives her Spanish students a test each week. Some of the students’ marks for two weeks are shown in the scatter diagram.

Leo scored 28 marks in week 1 and 30 marks in week 2.

On the scatter diagram, plot a point to show Leo’s marks.

Extract:

A teacher gives her Spanish students a test each week. Some of the students' marks for two weeks are shown in the scatter diagram.

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

Extract:

A teacher gives her Spanish students a test each week. Some of the students' marks for two weeks are shown in the scatter diagram.

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

Sonia scored 20 marks in week 1 but was absent in week 2.

Use your line of best fit to estimate a mark for Sonia in week 2.

The scatter diagram shows the number of people and the number of phones in each of 8 buildings.

One of the buildings contains 42 people.

Write down the number of phones in this building.

Extract:

The scatter diagram shows the number of people and the number of phones in each of 8 buildings.

What type of correlation is shown in the scatter diagram?

The table shows the maximum power, kW, and the time taken, in seconds, to accelerate from 0 to 100 km/h for each of 10 cars.

i) Find the range of the times.

........................................... s [1]

ii) Find the median maximum power.

........................................... kW [2]

Extract:

The table shows the maximum power, kW, and the time taken, in seconds, to accelerate from 0 to 100 km/h for each of 10 cars.

| Maximum power (kW) | 77 | 52 | 103 | 55 | 44 | 51 | 85 | 135 | 90 | 110 | | Time (seconds) | 12.5 | 14.9 | 9.0 | 12.1 | 14.4 | 12.9 | 10.0 | 7.1 | 11.0 | 9.4 |

i) Complete the scatter diagram. The first eight points have been plotted for you.

ii) What type of correlation is shown on the scatter diagram?

iii) Describe the relationship between the maximum power of a car and the time taken to accelerate from 0 to 100km/h.

iv) Draw a line of best fit on the scatter diagram.

v) Another car has a maximum power of 63kW.

Use your line of best fit to estimate the time taken for this car to accelerate from 0 to 100km/h.

............................................... s [1]

Mrs Salaman gives her class two mathematics tests. The scatter diagram shows information about the marks each student scored.

Write down the highest mark scored on test 1.

Extract:

Mrs Salaman gives her class two mathematics tests. The scatter diagram shows information about the marks each student scored.

Write down the type of correlation shown in the scatter diagram.

Extract:

Mrs Salaman gives her class two mathematics tests. The scatter diagram shows information about the marks each student scored.

Draw a line of best fit on the scatter diagram.

Extract:

Draw a line of best fit on the scatter diagram.

Hamish scored a mark of 40 on test 1. He was absent for test 2.

Use your line of best fit to find an estimate for his mark on test 2.

Belle records the height, in centimetres, and the mass, in kilograms, of some goats. Some of her results are shown in the scatter diagram.

The table shows four more results.

Plot these points on the scatter diagram.

Extract:

Belle records the height, in centimetres, and the mass, in kilograms, of some goats. Some of her results are shown in the scatter diagram.

What type of correlation is shown in this scatter diagram?

Extract:

Belle records the height, in centimetres, and the mass, in kilograms, of some goats.

Some of her results are shown in the scatter diagram.

The table shows four more results.

| Height (cm) | 23 | 30 | 36 | 38 | | Mass (kg) | 31.2 | 33.5 | 34.6 | 34.8 | Plot these points on the scatter diagram.

i) Draw a line of best fit on the scatter diagram.

ii) Use your line of best fit to estimate the height of a goat with mass 32.5kg.

Extract:

Belle records the height, in centimetres, and the mass, in kilograms, of some goats. Some of her results are shown in the scatter diagram. The table shows four more results. | Height (cm) | 23 | 30 | 36 | 38 |

Work out the percentage of the 12 goats that have a height between 26cm and 35cm.

Ten students eat cereal with milk for breakfast. The amounts are shown in the table.

i) Complete the scatter diagram. The first six points have been plotted for you.

ii) For these students, describe the relationship between the amount of cereal and the amount of milk.

iii) On the grid, draw a line of best fit.

iv)Another student has 280ml of milk with her cereal.

Use your line of best fit to estimate an amount of cereal this student has.

.............................................. g [1]

v) Explain why this scatter diagram should not be used to estimate the amount of milk for a student who has more than 70g of cereal.

The scatter diagram shows the age and value of each of ten cars, all of the same model.

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

$ ...................................................

13 high school basketball players recorded their scores in a game.

The table shows each player’s height (in cm) and the number of points they scored in the game.

Complete the scatter diagram using the points in the table.

The first eight points have already been plotted.

What type of correlation is shown in the scatter diagram?

Draw the line of best fit on the scatter diagram.

The table below shows the ages of some children and the total number of hours of sleep they had between noon on Saturday and noon on Sunday.

On the scatter diagram, plot the information from the table.

Extract:

The table below shows the ages of some children and the total number of hours of sleep they had between noon on Saturday and noon on Sunday.

Age (years)

3

2

5

4

1

6

8

5

4

Number of hours sleep

14.4

15.6

12.4

13.2

16.4

10.0

7.6

11.2

14.0

State the correlation that is shown in your scatter diagram.

Extract:

The table below shows the ages of some children and the total number of hours of sleep they had between noon on Saturday and noon on Sunday.

Age (years)

3

2

5

4

1

6

8

5

4

Number of hours sleep

14.4

15.6

12.4

13.2

16.4

10.0

7.6

11.2

14.0

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

Extract:

The table below shows the ages of some children and the total number of hours of sleep they had between noon on Saturday and noon on Sunday.

Age (years)

3

2

5

4

1

6

8

5

4

Number of hours sleep

14.4

15.6

12.4

13.2

16.4

10.0

7.6

11.2

14.0

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

A child who is 4 years sleeps between noon on Saturday and noon on Sunday.

Use your line of best fit to estimate how many hours they sleep.

Aisha records the distance she runs and her average speed. The results are shown in the scatter diagram.

The table shows the results of four more runs.

On the scatter diagram, plot these points.

Extract:

Aisha records the distance she runs and her average speed. The results are shown in the scatter diagram.

What type of correlation is shown in the scatter diagram?

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

Extract:

Aisha records the distance she runs and her average speed. The results are shown in the scatter diagram.

The table shows the results of four more runs.

| Distance (km) | 4.2 | 5.7 | 7.1 | 8.8 | | Average speed (km/h) | 13.4 | 11.8 | 9.8 | 8.3 |

Use your line of best fit to estimate her average speed when she runs a distance of 6km.

..........................km/h

Fourteen students each take two tests in French, a speaking test and a written test. The table shows the scores.

Complete the scatter diagram. The first ten points have been plotted for you.

What type of correlation is shown in this scatter diagram?

Extract:

| Speaking test | 10 | 13 | 48 | 30 | 35 | 18 | 41 | 40 | 22 | 28 | 20 | 44 | 37 | 46 | | Written test | 24 | 44 | 51 | 39 | 45 | 29 | 56 | 20 | 39 | 49 | 33 | 52 | 44 | 52 |

One student has a high score in the speaking test and a low score in the written test.

On the scatter diagram, put a ring around this point.

Extract:

Fourteen students each take two tests in French, a speaking test and a written test. The table shows the scores.

| Speaking test | 10 | 13 | 48 | 30 | 35 | 18 | 41 | 40 | 22 | 28 | 20 | 44 | 37 | 46 | | Written test | 24 | 44 | 51 | 39 | 45 | 29 | 56 | 20 | 39 | 49 | 33 | 52 | 44 | 52 | Complete the scatter diagram. The first ten points have been plotted for you.

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

Extract:

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

Use your line of best fit to estimate a score in the written test for a student who scored 25 in the speaking test.

The number of attempts at a driving test and the number of driving lessons for each of 17 people are shown in the scatter diagram.

i) What type of correlation is shown in the scatter diagram?

ii) One of these people is picked at random. Work out the probability that this person had 5 or more attempts.

iii) Draw a line of best fit on the scatter diagram.

iv) Another person had 15 lessons. Estimate their number of attempts.

Lucy asked 12 people how many hours they each spent playing a computer game and the number of levels they each completed in one month.

The results are shown in the table.

Complete the scatter diagram. The first eight points have been plotted for you.

Extract:

| Time spent playing (hours) | 90 | 32 | 70 | 75 | 30 | 70 | 40 | 80 | 40 | 65 | 50 | 32 | | Number of levels completed | 22 | 5 | 12 | 17 | 6 | 7 | 18 | 20 | 8 | 15 | 11 | 9 |

One person completes more levels per hour than any of the others.

On the scatter diagram, put a ring around the point for this person.

Extract:

Lucy asked 12 people how many hours they each spent playing a computer game and the number of levels they each completed in one month.

The results are shown in the table.

| Time spent playing (hours) | 90 | 32 | 70 | 75 | 30 | 70 | 40 | 80 | 40 | 65 | 50 | 32 | | Number of levels completed | 22 | 5 | 12 | 17 | 6 | 7 | 18 | 20 | 8 | 15 | 11 | 9 |

Complete the scatter diagram.

The first eight points have been plotted for you.

What type of correlation does this scatter diagram show?

Extract:

Lucy asked 12 people how many hours they each spent playing a computer game and the number of levels they each completed in one month.

The results are shown in the table.

| Time spent playing (hours) | 90 | 32 | 70 | 75 | 30 | 70 | 40 | 80 | 40 | 65 | 50 | 32 | | Number of levels completed | 22 | 5 | 12 | 17 | 6 | 7 | 18 | 20 | 8 | 15 | 11 | 9 |

Complete the scatter diagram.

The first eight points have been plotted for you.

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

Extract:

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

Another person, Monika, completed 19 levels but forgot to record the time spent playing.

Use your line of best fit to estimate the number of hours that Monika spent playing.

............................ hours [1]

The scatter diagram shows the value, in thousands of dollars, of eight houses in 1996 and the value of the same houses in 2016.

One of these eight houses had a value of $70000 in 1996. Write down the value of this house in 2016.

$ .................................

The values of two more houses are shown in the table.

On the scatter diagram, plot these values.

On the scatter diagram, draw a line of best fit

Extract:

The scatter diagram shows the value, in thousands of dollars, of eight houses in 1996 and the value of the same houses in 2016. On the scatter diagram, draw a line of best fit

Another house had a value of $50000 in 1996.

Find an estimate of the value of this house in 2016.

$ ............................... [1]