Scatter diagrams

Some houses in a village have new driveways laid by DriveDown. The scatter diagram shows the area and cost of each driveway.

Two of these houses have the same area of driveway.

Calculate the difference in the cost of the new driveway for these two houses.

Another house in the village has a driveway of area 25 m².

Estimate the cost of having a new driveway laid by DriveDown for this house.

Some houses in a village have new driveways laid by DriveDown.

The scatter diagram shows the area and cost of each driveway.

The measurements of Gwenda’s driveway are shown below.

Consider the exact area of Gwenda’s driveway. Calculate an estimate of how much it would cost Gwenda to have a new driveway laid by DriveDown.

You must show all your working.

Tanya’s driveway covers an area of 23 m². She decides to have her driveway repaired instead of having a new driveway.

Tanya thinks the repair will cost her 40% of the estimated cost of having a new driveway laid by DriveDown. She has budgeted £575 for the repair of her driveway. Will Tanya’s budget cover the cost of repairing her driveway?

Yes No

You must show all your working and give a reason for your answer.

Anwen has an outdoor mobile coffee stall.

Give the coordinates of the point through which a line of best fit should be drawn.

Hence, draw a line of best fit on the scatter diagram.

Coordinates of the point are (_........ ,_........ )

Estimate the number of cups of coffee that Anwen expects to sell on a day when the rainfall is 2·0 mm.

Use your line of best fit to find your estimate.

Number of cups of coffee is_........

The height of the storage space under Anwen’s serving counter is 97·5 cm, correct to the nearest 0·5 cm.

Anwen is going to buy a recycling bin of height exactly 97·3 cm. Can Anwen be certain that she can fit this bin under her serving counter?

Yes
No
Can’t decide

You must show working to support your answer.

Anwen has an outdoor mobile coffee stall.

Give the coordinates of the point through which a line of best fit should be drawn.

Hence, draw a line of best fit on the scatter diagram.

Coordinates of the point are (_........ ,_........ )

Estimate the number of cups of coffee that Anwen expects to sell on a day when the rainfall is 2·0 mm.

Use your line of best fit to find your estimate.

Number of cups of coffee is_........

The height of the storage space under Anwen’s serving counter is 97·5 cm, correct to the nearest 0·5 cm.

Anwen is going to buy a recycling bin of height exactly 97·3 cm. Can Anwen be certain that she can fit this bin under her serving counter?

Yes
No
Can’t decide

You must show working to support your answer.

Two of the remotes have the same width.

Write down the width and lengths of these remotes.

Width_........ cm

Lengths are_........ cm and_........ cm.

How is it best to describe the correlation seen in this scatter diagram?

Draw a line of best fit on the scatter diagram.

Two of the remotes have the same width.

Write down the width and lengths of these remotes.

Width_........ cm

Lengths are_........ cm and_........ cm.

Consider the remote with a width of 4.5 cm. Write down the ratio of the width of this remote to its length.

Give your answer in its simplest form.

How is it best to describe the correlation seen in this scatter diagram?

Draw a line of best fit on the scatter diagram.

Hubert has a quote from a gardener to landscape his garden. The gardener will charge a total of £175, excluding VAT. This total charge includes £55 for plants. The remainder of the charge is for labour.

The gardener says it will take 8 hours to landscape Hubert’s garden.

Calculate how much per hour the gardener is charging for labour.

VAT at 20% is payable on the charge of £175.

Calculate the total charge of the landscaping, including the VAT.

Is it possible to estimate the number of leaves on a flower of height 6 cm?

Yes No

You must give a reason for your answer.

How tall is the flower with the greatest number of leaves?

Circle your answer.

26 cm 2∙5 cm 7∙5 cm 5 cm 17∙5 cm

There are two flowers that each have 19 leaves. Calculate the difference in the heights of these two flowers.

You must show all your working.

Difference in the heights is_........ cm

Calculate the percentage of the flowers that have fewer than 23 leaves.

_........ % of the flowers have fewer than 23 leaves.

Myra recorded the wingspan and mass of a number of birds.

Her results are shown in the scatter diagram below.

The wingspan of one of the birds shown in the scatter diagram is 31 cm.

What is the mass of this bird?

Two of the birds shown in the scatter diagram have a mass of 5 g.

What is the difference between the wingspans of these two birds?

Difference between the wingspans is_........ cm

Use 30 cm ≈ 12 inches to answer this question.

Find the wingspan of the bird with a mass of 8·5 g.

Give your answer in inches.

Wingspan is_........ inches

What type of correlation does this scatter diagram show?

Use the scatter diagram to estimate the wingspan of a bird with a mass of 12 g.

Myra recorded the wingspan and mass of a number of birds.

Her results are shown in the scatter diagram below.

The wingspan of one of the birds shown in the scatter diagram is 31 cm.

What is the mass of this bird?

Two of the birds shown in the scatter diagram have a mass of 5 g.

What is the difference between the wingspans of these two birds?

Difference between the wingspans is_........ cm

Use 30 cm ≈ 12 inches to answer this question. Find the wingspan of the bird with a mass of 8.5 g.

Give your answer in inches.

Wingspan is_........ inches

What type of correlation does this scatter diagram show?

Use the scatter diagram to estimate the wingspan of a bird with a mass of 12 g.

In a science lesson, 13 students calculated an estimate of the area of their skin. The results are shown on the scatter diagram below.

Area of skin (m²)

Arwyn is the only student who made an error in his calculation. He is one of the tallest students. What is Arwyn’s calculated estimate of the area of his skin?

Circle your answer.

Which term best describes the correlation between a person’s height and the estimate of the area of their skin?

Circle your answer.

No correlation Spread Certain Positive Negative

Garth is 5 cm taller than Ella. The calculated estimate of the area of Ella’s skin is 1∙54 m².

How tall is Garth?

Garth is_{………........ ………………} m tall

In a science lesson, 13 students calculated an estimate of the area of their skin. The results are shown on the scatter diagram below.

Area of skin (m²)

Arwyn is the only student who made an error in his calculation. He is one of the tallest students. What is Arwyn’s calculated estimate of the area of his skin?

Circle your answer.

Which term best describes the correlation between a person’s height and the estimate of the area of their skin?

Circle your answer.

No correlation Spread Certain Positive Negative

Garth is 5 cm taller than Ella. The calculated estimate of the area of Ella’s skin is 1∙54 m².

How tall is Garth?

Garth is_{………........ ………………} m tall

Bryn is 1∙50 m tall. Abigail is 18% taller than Bryn.

Find Abigail’s calculated estimate of the area of her skin.

Abigail’s estimate of the area of her skin is_{………........ ………………} m²

In a science lesson, 13 students calculated an estimate of the area of their skin.

The results are shown on the scatter diagram below.

Area of skin (m²)

Bryn is 1∙50 m tall. Abigail is 18% taller than Bryn.

Find Abigail’s calculated estimate of the area of her skin.

Abigail’s estimate of the area of her skin is_{………........ ………………} m²

Rosie recorded the rainfall and the number of hours of sunshine each day last week.

On one day last week, the number of hours of sunshine was low and the rainfall was lower than on any other day. Which day was it?

Circle your answer.

Saturday Sunday Monday Tuesday Can’t tell

Rosie says,

Is Rosie correct?

Yes No

You must give a reason for your answer.

At 3 p.m. each day last week, Rosie recorded the wind speed and the number of birds feeding in her garden.

Was there a correlation between wind speed and the number of birds feeding in Rosie’s garden last week?

Yes No

You must give a reason for your answer.

The greatest wind speed at 3 p.m. last week was on Tuesday.

How many birds were feeding in Rosie’s garden at this time?

On Wednesday last week, the wind speed at 3 p.m. was a quarter of that on Friday.

Complete the following table.

Rosie recorded the rainfall and the number of hours of sunshine each day last week.

Rosie says,

Is Rosie correct?

Yes No

You must give a reason for your answer.

At 3 p.m. each day last week, Rosie recorded the wind speed and the number of birds feeding in her garden.

On Wednesday last week, the wind speed at 3 p.m. was a quarter of that on Friday.

Complete the following table.

Some students were asked to select an even number between 0 and 100.

The heights of these students and the number they each selected are shown in the scatter diagram below.

Describe the correlation shown by the scatter diagram.

Gwenda and Daniel selected the same number. Gwenda is shorter than Daniel. Lotte is the shortest student. Iona and Steffan are both the same height. Iona selected a number greater than 40.

Complete the table.

Some students were asked to select an even number between 0 and 100.

The heights of these students and the number they each selected are shown in the scatter diagram below.

Describe the correlation shown by the scatter diagram.

Gwenda and Daniel selected the same number. Gwenda is shorter than Daniel. Lotte is the shortest student. Iona and Steffan are both the same height. Iona selected a number greater than 40.

Complete the table.

The distance a car will travel using 1 gallon of fuel is called its fuel economy.

The fuel economy of a number of cars with different engine sizes is shown below.

Fuel economy (miles per gallon)

Use the scatter diagram to answer the following questions.

State the fuel economy of the car with the largest engine size.

Fuel economy_........ miles per gallon

State the engine size of the car with a fuel economy of 42 miles per gallon.

Engine size_........ litres

Draw, by eye, a line of best fit on the scatter diagram.

The distance a car will travel using 1 gallon of fuel is called its fuel economy.

The fuel economy of a number of cars with different engine sizes is shown below.

Fuel economy (miles per gallon)

Use the scatter diagram to answer the following questions.

State the fuel economy of the car with the largest engine size.

Fuel economy_........ miles per gallon

State the engine size of the car with a fuel economy of 42 miles per gallon.

Engine size_........ litres

Calculate the mean fuel economy of the 5 cars with the smallest engine sizes. [3]

Mean fuel economy is_........ miles per gallon

Draw, by eye, a line of best fit on the scatter diagram.

Complete each of the statements below.

‘In July 2005, two of the 8 towns had the same number of people. The percentages of rubbish recycled in these two towns were

........ % and........ %.’

‘The town with the least number of people had set a target of recycling 45% of rubbish for July 2005. This small town beat this target by........ %’

Explain why it is not reasonable to use this data to estimate the percentage of rubbish

recycled in a town of 9000 people.

Lekan’s parents have complained that they are paying too much towards his mobile phone bill each month.

Lekan decides to ask a number of students in school how much their parents or carers pay towards their mobile phone bills each month. He displays the results in a scatter diagram. These include his own results.

Lekan’s parents want to know the names of some of these students.

The two 15-year-old students are Harriet and Eleri. Eleri is older than Harriet.

Gwilym and Aled’s parents each pay £27.50 per month. Aled is younger than Gwilym.

21 21

Complete each of the following statements.

‘Eleri’s parents or carers pay £_{………........ ……….} each month towards her mobile phone bill.’

‘Harriet’s parents or carers pay £_{………........ ……….} each month towards her mobile phone bill.’

Complete each of the following statements.

‘Gwilym is_{………........ ….} years_{………........ ….} months old.’

‘Aled is_{………........ ….} years_{………........ ….} months old.’

Lekan’s parents pay £32.50 per month towards his mobile phone bill. He is the youngest of the 3 students who receive £32.50 per month towards their mobile phone bill.

How old is Lekan?

Do you think Lekan’s parents are right to complain that they are paying too much towards his mobile phone bill each month?

You must use the scatter diagram to give a reason for your answer.

Yes No

Lekan’s parents have complained that they are paying too much towards his mobile phone bill each month.

Lekan decides to ask a number of students in school how much their parents or carers pay towards their mobile phone bills each month. He displays the results in a scatter diagram. These include his own results.

Lekan’s parents want to know the names of some of these students.

The two 15-year-old students are Harriet and Eleri. Eleri is older than Harriet.

Gwilym and Aled’s parents each pay £27.50 per month. Aled is younger than Gwilym.

Complete each of the following statements.

‘Eleri’s parents or carers pay £_{………........ ……….} each month towards her mobile phone bill.’

‘Harriet’s parents or carers pay £_{………........ ……….} each month towards her mobile phone bill.’

Complete each of the following statements.

‘Gwilym is_{………........ ….} years_{………........ ….} months old.’

‘Aled is_{………........ ….} years_{………........ ….} months old.’

Lekan’s parents pay £32.50 per month towards his mobile phone bill. He is the youngest of the 3 students who receive £32.50 per month towards their mobile phone bill.

How old is Lekan?

Do you think Lekan’s parents are right to complain that they are paying too much towards his mobile phone bill each month?

You must use the scatter diagram to give a reason for your answer.

Yes No

Ffion thinks that the taller you are, the greater your waist measurement will be.

She recorded the height and waist measurements, in centimetres, for 6 people.

Give one reason why using this scatter graph to estimate the waist measurement of other

people is unlikely to give reliable results.

Ffion thinks that the taller you are, the greater your waist measurement will be.

She recorded the height and waist measurements, in centimetres, for 6 people.

Draw a scatter diagram to display these measurements.

Use the graph paper below.

Give one reason why using this scatter graph to estimate the waist measurement of other

people is unlikely to give reliable results.

A group of friends measured the heights and masses of their pets.

The scatter diagram shows the results.

Mass (kg)

Describe the correlation shown by this scatter diagram.

The friends notice that the tallest pet has the same mass as another pet.

What is the height of this other pet?

Students are taking tests in English and Welsh. The English test is marked out of 80. The Welsh test is marked out of 70.

Dyfed scores 35 in his English test. Estimate Dyfed’s score as a percentage.

Circle your answer.

4% 20% 23% 44% 51%

Liam scores 22 in his Welsh test. Estimate Liam’s score as a percentage.

Circle your answer.

Rowena states a hypothesis, ‘Boys do better than girls in their English tests.’

She displays the test marks for 5 girls and 5 boys in scatter diagrams.

Boys’ test results Mark in Welsh

Does the data support Rowena’s hypothesis?

You must give a reason for your answer.

How could Rowena improve the testing of her hypothesis?

Students are taking tests in English and Welsh. The English test is marked out of 80. The Welsh test is marked out of 70.

Dyfed scores 35 in his English test. Estimate Dyfed’s score as a percentage.

Circle your answer.

4% 20% 23% 44% 51%

Liam scores 22 in his Welsh test. Estimate Liam’s score as a percentage.

Circle your answer.

Rowena states a hypothesis, ‘Boys do better than girls in their English tests.’

She displays the test marks for 5 girls and 5 boys in scatter diagrams.

Boys’ test results Mark in Welsh

Does the data support Rowena’s hypothesis?

You must give a reason for your answer.

How could Rowena improve the testing of her hypothesis?