Scatter graphs Quiz (Grade 4)

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Score: 0 / 10

Scatter graphs — Notes & Worked Examples Show / Hide

Explanation:

A scatter graph plots pairs of values to investigate whether two variables are related. Correlation can be positive (as one increases, the other increases), negative (as one increases, the other decreases), or no correlation. An outlier is an isolated point that does not fit the general trend.

Always draw a straight line of best fit with a ruler through the middle of the points (ignoring any outliers) before estimating a value. Estimating within the data range (interpolation) is reliable; estimating outside the data range (extrapolation) is unreliable because the trend may not continue.

Example 1: A scatter graph plots engine size (L) against fuel efficiency (mpg). State the correlation and describe the relationship.

Negative correlation.

As engine size increases, mpg decreases.

Example 2: Ice cream sales (£) are plotted from 12°C to 26°C. Estimate sales at 20°C, and explain why estimating at 38°C is unreliable.

At 20°C: £160.

38°C is outside data range (extrapolation).

One Page Guide (PDF) Scatter graphs Worksheets

Question 1

[2 marks]

The scatter graph shows the maximum temperature and the number of hours of sunshine in fourteen British towns on one day.

(a) Write down the coordinates of this point. [1 mark]

(b) For all the other points write down the type of correlation. [1 mark]

Worked Solution & Answer

(a)

Outlier is at (10, 19) B1

Answer (a): 10, 19

(b)

Points slope upwards from left to right -> positive correlation B1

Answer (b): Positive

Question Paper (PDF) • Mark Scheme (PDF)

Question 2 AQA Jun 2022 3H Q3

[2 marks]

Here are four scatter graphs.

(a) For which graph is a straight line of best fit appropriate?
A B C D [1 mark]

(b) Which graph has one outlier?
A B C D [1 mark]

Worked Solution & Answer

(a)

Graph D shows a clear linear correlation (negative slope) where points scatter along a straight line. B1

Answer (a): D

(b)

Graph B shows points closely following a curved downward trend except for one isolated point well away from the curve. B1

Answer (b): B

Question Paper (PDF) • Mark Scheme (PDF)

Question 3 AQA Nov 2022 3F Q21

[3 marks]

The scatter graph shows the height and mass of some dogs.

(a) The scatter graph shows positive correlation.
Describe the relationship between the height and mass of the dogs. [1 mark]

Relationship

(b) Use a line of best fit to estimate the mass of a dog with height 48 cm [2 marks]

Answer kg

Worked Solution & Answer

(a)

As height increases, mass increases. B1

Answer (a): Relationship Taller dogs tend to have a greater mass

(b)

Draw a line of best fit through the points M1
At height = 48 cm, read across to the vertical axis to find mass ≈ 21 kg (acceptable range 20 kg to 22 kg). A1

Answer (b): Answer 21 kg

Question Paper (PDF) • Mark Scheme (PDF)

Question 4

[3 marks]

The scatter graph shows information about the volume of traffic and the carbon monoxide level at a point on a road each day for 22 days.

(a) Write down the coordinates of this point. [1 mark]

(b) Estimate the carbon monoxide level for this day. [2 marks]

mg/m³

Worked Solution & Answer

(a)

Outlier at (100, 18) B1

Answer (a): (100, 18)

(b)

Draw line of best fit M1
read off at x = 370 ⇒ ~13.8 mg/m³ A1

Answer (b): 13.8 mg/m³

Question Paper (PDF) • Mark Scheme (PDF)

Question 5

[3 marks]

The scatter graph shows information about some ships.
It shows the length and the width of each ship.

(a) What type of correlation does this scatter graph show? [1 mark]

(b) Draw a line of best fit on the scatter graph. [1 mark]

metres

Worked Solution & Answer

(a)

positive

Answer (a): positive

(b)

Line of best fit drawn

Answer (b): Line of best fit drawn

(c)

At length = 194 m, line of best fit gives ~28 m B1

Answer (c): 28 metres

Question Paper (PDF) • Mark Scheme (PDF)

Question 6 AQA Nov 2023 1F Q24 / 1H Q6

[4 marks]

A music company releases 10 albums.
The scatter graph shows, for each album,
• the number of downloads on the first day
and
• the number of CDs sold on the first day.
A line of best fit has been drawn on the scatter graph.

(a) The scatter graph shows positive correlation.
Describe the relationship between number of downloads and number of CDs sold. [1 mark]

(b) The company earns
• £2.50 for each download
and
• £3 for each CD sold.
The company releases another album.
On the first day it has 9000 downloads.
Estimate the **total** amount the company earns from downloads and CDs of the album that day. [3 marks]

Answer £

Worked Solution & Answer

(a)

As the number of downloads increases, the number of CDs sold increases

Answer (a): As the number of downloads increases, the number of CDs sold increases

(b)

From the line of best fit at 9000 downloads, number of CDs sold = 5500 M1
Earnings from downloads = 9000 × £2.50 = £22 500 M1
Earnings from CDs = 5500 × £3 = £16 500
Total = £22 500 + £16 500 = £39 000 A1

Answer (b): Answer £ 39 000

Question Paper (PDF) • Mark Scheme (PDF)

Question 7 AQA Jun 2018 2F Q18

[4 marks]

A shop sells raincoats and umbrellas.
The scatter graph shows the monthly sales for 12 months.

(a) Write down the type of correlation shown by the graph. [1 mark]

Answer

(b) The manager expects the sales of umbrellas next month to be £60
Draw a line of best fit to estimate the sales of raincoats next month. [3 marks]

Answer £

Worked Solution & Answer

(a)

The points trend upwards from left to right, indicating positive correlation. B1

Answer (a): Answer Positive

(b)

Draw a straight line of best fit through the points M2
Read the raincoat sales value corresponding to umbrella sales of £60: approximately £125 (or range £120 to £130). A1

Answer (b): Answer £ 125

Question Paper (PDF) • Mark Scheme (PDF)

Question 8 AQA Jun 2023 1F Q20

[4 marks]

Players score points in a game.
The scatter graph shows the time played and the points scored by some players.

(a) Circle the strength and type of correlation shown.
weak positive strong positive weak negative strong negative [1 mark]

(b) Players get one extra life for every 2000 points they score.
Jonah plays the game for 15 hours.
Use a line of best fit to estimate the number of extra lives he gets. [3 marks]

Answer

Worked Solution & Answer

(a)

The points lie close to an upward sloping straight line, indicating strong positive correlation. B1

Answer (a): strong positive

(b)

Using a line of best fit at 15 hours, estimated points ≈ 34 000 (or 32,000 to 36,000) M2
Number of extra lives = 34 000 ÷ 2000 = 17 (or 16 to 18). A1

Answer (b): Answer 17

Question Paper (PDF) • Mark Scheme (PDF)

Question 9 AQA Nov 2019 2F Q25 / 2H Q6

[4 marks]

The scatter graph shows the best high jump and the best long jump for 15 boys.

(a) Write down the type of correlation shown. [1 mark]

Answer

(b) Liam has a best high jump of 166 cm.
Use a line of best fit to estimate his best long jump. [2 marks]

Answer cm

(c) Another boy has a best high jump of 195 cm.
Give a reason why you should not use a line of best fit to estimate his best long jump. [1 mark]

Worked Solution & Answer

(a)

As high jump increases, long jump generally increases, showing positive correlation. B1

Answer (a): Answer Positive

(b)

Drawing a line of best fit through the points and reading at x = 166 gives approximately 534 cm (or 530 to 538 cm). M1 A1

Answer (b): Answer 534 cm

(c)

195 cm is beyond the maximum high jump recorded in the data (185 cm), so predicting this value requires extrapolation which is unreliable. C1

Answer (c): It is outside the range of the data (extrapolation)

Question Paper (PDF) • Mark Scheme (PDF)

Question 10 Eduqas Nov 2019 1F Q11

[4 marks]

Anisha wants to compare the number of days it rained each month, in Anstown and Beeham, in 2018.
Anisha has plotted the data for the first 6 months on the scatter graph below.
The data for the last 6 months is given in the table:
@@TABULAR₀@@

(a) Plot the data for the last 6 months on the scatter graph. [2 marks]

(b) What does your scatter graph show about the relationship between the number of days it rained in Anstown and the number of days it rained in Beeham? [1 mark]

Worked Solution & Answer

(a)

Plot each pair of coordinates from the table on the scatter graph. M1 A1

Answer (a): 6 points correctly plotted: (4, 7), (9, 9), (8, 6), (13, 10), (14, 12), (15, 13)

(b)

The points trend upwards from left to right, indicating positive correlation. B1

Answer (b): Positive correlation (as rainfall in Anstown increases, rainfall in Beeham increases)

(c)

Points with x ≥ 11 and y ≥ 11: (12, 12), (15, 11), (14, 12), (15, 13) ⇒ 4 months. B1

Answer (c): 4

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Score: 0 / 10 (0 / 33 marks)

Scatter graphs Worksheets Next: Probability →

Grade 4 Quizzes

24 Topics

4A - Compound interest	4B - Indices (index laws)
4C - Prime factors HCF and LCM	4D - Real life graphs
4E - Inequalities on a number line	4F - Solving inequalities
4G - Forming and solving equations	4H - nth term of a linear sequence
4J - Expanding and factorising	4K - Pythagoras theorem
4L - Angles in parallel lines	4M - Angles in polygons
4N - Surface area	4P - Volume of a cuboid
4Q - Volume of a prism	4R - Bearings
4S - Cylinders	4T - Plans and elevations
4U - Scatter graphs	4V - Probability
4W - Averages from tables	4X - Reverse mean
4Y - Area of a trapezium	4Z - Loci and construction