KS3 Maths · Year 8 · Chapter 4: Using data · Lesson 1

Scatter graphs and correlation

Year 8About 60 minutesNo calculator45 marks

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Date

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Quick questions to start.

A1
Last lesson
Two regular octagons are placed side by side at a point. Work out the size of the gap.
[1 mark]
Answer
A2
Needed today
A line goes through $(0, 4)$ and goes up $3$ for every $1$ across. Work out its height when $x = 5$ .
[1 mark]
Answer
A3
Year 7
Work out the mean of $12$ , $15$ , $18$ and $23$ .
[1 mark]
Answer
A4
From chapter 1
Increase $£80$ by $15%$ .
[1 mark]
Answer

Example, then your turn

Year 8

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

Example 1

The scatter graph shows the age and the value of $8$ cars. Describe the correlation. What does it tell you?

Hint As one value goes up, does the other go up, go down, or neither?

B1
The scatter graph shows the height and the arm span of $8$ people. Describe the correlation. What does it tell you?
[2 marks]

Example 2

Sales of ice cream have positive correlation with temperature. Sales of hot drinks have negative correlation with temperature. What correlation would you expect between sales of ice cream and sales of hot drinks?

Hint Think about a hot day. What happens to each kind of sale?

B2
Sales of scarves have negative correlation with temperature. Sales of hot chocolate have negative correlation with temperature. What correlation would you expect between sales of scarves and sales of hot chocolate? Give a reason.
[2 marks]

Example 3

The graph shows the temperature and the number of visitors to a park on $8$ days, with a line of best fit. Estimate the number of visitors on a day when the temperature is $17^{\circ} C$ .

Hint Go up from

17

on the temperature axis to the line, then across to the other axis.

B3
The graph shows the distance and the time of $8$ taxi journeys, with a line of best fit. Estimate the time of a $9$ km journey.
[2 marks]
Answer $\dots\dots$ minutes

Example 4

A line of best fit for some children aged $8$ to $15$ shows their reading age. Explain why it should not be used to estimate the reading age of a $30$ -year-old.

Hint Look at which ages the data covers.

B4
The data for the taxi journeys in B3 runs from $2$ km to $16$ km. Explain why the line of best fit should not be used to estimate the time of a $60$ km journey.
[2 marks]

Practice

Year 8

C1
$A$ has positive correlation with $B$ . $B$ has negative correlation with $C$ . What correlation would you expect between $A$ and $C$ ?
[2 marks]
Answer
C2
$P$ has no correlation with $Q$ . $Q$ has positive correlation with $R$ . What can you say about $P$ and $R$ ?
[2 marks]
Answer

C3
The graph shows the hours of homework and the hours of TV watched by $8$ students in a week, with a line of best fit. Estimate the hours of homework done by a student who watches $20$ hours of TV in a week.
[2 marks]
Answer $\dots\dots$ hours
C4
The table shows the shoe size (Size) and the height in cm (Height) of $7$ students. One student does not fit the pattern. Who is it? Give a reason.
[2 marks]
C5
Which pair would have negative correlation? A: height and shoe size. B: age of a car and its value. C: house number and test mark. Give a reason.
[2 marks]
C6
The table shows the hours of exercise a week and the resting heart rate (beats a minute) of $6$ people. Describe the correlation and say what it means.
[2 marks]

Exam-style questions

GCSE Foundation

D1
Ice cream sales and the number of people with sunburn have positive correlation. Lena says, "This shows that eating ice cream causes sunburn."
Explain why Lena is wrong.
[2 marks]

D2
The scatter graph shows the age and the time to run $100$ m for $8$ children, with a line of best fit.
(a)
Describe the correlation.
[1 mark]
Answer
(b)
Estimate the time for an $11$ -year-old.
[2 marks]
Answer $\dots\dots$ seconds
(c)
A child runs $100$ m in $13$ seconds. Estimate the child's age.
[2 marks]
Answer $\dots\dots$ years
(d)
Explain why the line should not be used for a $4$ -year-old.
[2 marks]
Total for D2: 7 marks
D3
In a study of football teams, points gained has positive correlation with goals scored, and negative correlation with goals conceded.
(a)
What correlation would you expect between goals scored and goals conceded?
[2 marks]
Answer
(b)
A team concedes very few goals. What would you expect about the number of points it gains? Give a reason.
[2 marks]
Total for D3: 4 marks
D4
The scatter graph shows the maths mark and the art mark of $9$ students.
(a)
Describe the correlation.
[1 mark]
Answer
(b)
Ali says, "I got $80$ in maths, so the graph shows I will get about $80$ in art." Explain why Ali is wrong.
[3 marks]
Total for D4: 4 marks

Extension

Stretch

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

E1
A line of best fit goes through the points $(0, 10)$ and $(8, 50)$ . There is no graph. Use the line to estimate $y$ when $x = 13$ , and $x$ when $y = 35$ .
[4 marks]
Hint 1 · What to try
From $x = 0$ to $x = 8$ the line goes up $50 - 10 = 40$ .
Hint 2 · The first line
So the line goes up $40 \div 8 = 5$ for every $1$ across, starting from $10$ .
Hint 3 · The full method
For $y = 35$ : $35 - 10 = 25$ above the start, and $25 \div 5$ .
Answer $y = \dots\dots$ $x = \dots\dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can describe the correlation on a scatter graph and say what it means.
I can work out the correlation between two things from two other correlations.
I can use a line of best fit to make an estimate, and say when not to.

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