GCSE Maths · Higher · Chapter 3: Statistical diagrams and averages · Lesson 3

Scatter diagrams and correlation

Grades 4–7About 45 minutesCalculator allowed32 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Find the midpoint of $(- 2, 0)$ and $(8, 10)$ .
[1 mark]
Answer
A2
Last lesson
Pets owned: $1$ by 2 people, $2$ by 5, $3$ by 5. Find the total number of pets.
[1 mark]
Answer
A3
From chapter 1
Find the lowest common multiple of $8$ and $12$ .
[1 mark]
Answer
A4
From chapter 3
A pie chart shows 90 people. A sector has angle $7 2^{\circ}$ . How many people is that?
[1 mark]
Answer

Grades 5–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

Five readings: $(4, 11)$ , $(8, 18)$ , $(12, 26)$ , $(16, 31)$ , $(20, 39)$ . Find the point the line of best fit passes through.

Hint The line goes through the mean point: the mean

x

with the mean

y

B1
Five readings: $(6, 22)$ , $(9, 27)$ , $(13, 31)$ , $(18, 40)$ , $(24, 50)$ . Find the point the line of best fit passes through.
[3 marks]
Answer $(\dots\dots, \dots\dots)$

Example 2

A line of best fit is $y = 2.5 x + 9$ , from readings with $x$ from $4$ to $20$ . Estimate $y$ at $x = 12$ , and say whether $x = 40$ can be trusted.

Hint Put the value in. Then ask whether

x = 40

is inside the readings.

B2
A line of best fit is $y = 1.8 x + 6$ , from readings with $x$ from $5$ to $25$ . Estimate $y$ at $x = 18$ , and say whether $x = 60$ can be trusted.
[3 marks]

Grades 5–6

C1
A line of best fit for test mark $y$ against hours of revision $x$ is $y = 7 x + 22$ . What does the $7$ tell you?
[1 mark]
C2
A line of best fit passes through $(10, 24)$ and $(40, 60)$ . Find its gradient.
[2 marks]
Answer

C3
A line of best fit is $y = 0.4 x + 15$ . Find $x$ when $y = 31$ .
[2 marks]
Answer
C4
Hat sales and soup sales both rise together. Explain why one need not cause the other.
[2 marks]

Grades 6–7

D1
For children aged $5$ to $11$ , the line of best fit for height $h$ cm against age $a$ years is $h = 6 a + 80$ . Ben says, "So a $40$ -year-old is $320$ cm tall."
Explain why Ben's estimate cannot be trusted.
[2 marks]

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can describe the correlation on a scatter diagram and spot an outlier.
I can find the mean point a line of best fit passes through.
I can read an estimate off a line of best fit and say when it is unreliable.

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