KS3 Maths · Year 7 · Chapter 9: Interpreting data · Lesson 4

Creating scatter graphs

Year 7About 70 minutesNo calculator45 marks

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Quick questions to start.

A1
Needed today
The points $(2, 5)$ , $(4, 9)$ and $(6, 13)$ lie on a straight line. What is $y$ when $x = 5$ ?
[1 mark]
Answer
A2
Needed today
On an axis, $5$ small squares stand for $10$ . A point is $3$ small squares above $20$ . What value is it at?
[1 mark]
Answer
A3
Last lesson
The older a car, the lower its value. What type of correlation is this?
[1 mark]
Answer
A4
From chapter 8
Round $0.04782$ to $2$ significant figures.
[1 mark]
Answer

Example, then your turn

Year 7

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

Example 1

Arm span and height, in cm, of $8$ pupils: $(142, 143)$ , $(145, 144)$ , $(150, 151)$ , $(152, 150)$ , $(158, 160)$ , $(160, 158)$ , $(165, 166)$ , $(170, 169)$ . Plot the points and describe the correlation.

Hint Each pair is (arm span, height): go across to the arm span, then up to the height. Each small square is

2

cm.

B1
Temperature (°C) and hot chocolates sold on $8$ days: $(2, 44)$ , $(4, 40)$ , $(6, 38)$ , $(8, 30)$ , $(10, 28)$ , $(12, 22)$ , $(14, 20)$ , $(16, 14)$ . On the grid, plot the points. Describe the correlation and say what it tells you.
[4 marks]
AnswerCorrelation: $\dots$

Example 2

The graph shows the hours $9$ pupils revised and their marks, with a line of best fit.

(a) Estimate the mark for $2.5$ hours of revision.
(b) Estimate the hours revised for a mark of $50$ .
(c) Can the line estimate the mark for $30$ hours?

Hint Go from the value you know to the LINE, not to a point. Then go across (or down) to the other axis.

B2
The graph shows how far $10$ pupils live from school and how long they take, with a line of best fit.
(a) Estimate the time for $7.5$ km.
(b) Why is the line no use for a pupil who lives $40$ km away?
[3 marks]
Answer(a) $\dots$ min

Example 3

Three lines, A, B and C, are drawn on the same scatter graph. Which is the best line of best fit? Say what is wrong with the other two.

Hint A good line follows the trend, with about as many points above it as below it. It does not have to pass through

(0, 0)

B3
Ravi joins the first and last points to make his line of best fit. Is it a good line? Give a reason.
[2 marks]

Practice

Year 7

C1
A line of best fit passes through $(0, 12)$ and $(20, 52)$ . Estimate $y$ when $x = 15$ , and $x$ when $y = 32$ .
[2 marks]
Answer $y = \dots$ , $x = \dots$
C2
Give two things that make a line of best fit a good one.
[2 marks]

C3
One point on a scatter graph is far away from all the others. Should Kim make her line of best fit pass through it? Explain.
[2 marks]
C4
A tree's age (years) and the leaves on one branch: $(10, 45)$ , $(20, 40)$ , $(30, 30)$ , $(40, 25)$ , $(50, 15)$ . On the grid, plot the points and draw a line of best fit.
[3 marks]

Exam-style questions

GCSE Foundation

D1
The graph shows the marks of $11$ pupils in two tests, with a line of best fit. Some pupils missed one of the tests.
(a)
Dan scored $40$ in test A and missed test B. Eve scored $21$ in test B and missed test A. Estimate Dan's test B mark and Eve's test A mark.
[2 marks]
AnswerDan $\dots$ , Eve $\dots$
(b)
Fay scored $2$ in test A. Why would an estimate of her test B mark be less reliable?
[2 marks]
Total for D1: 4 marks

D2
Length (cm) and mass (g) of $9$ fish: $(12, 40)$ , $(15, 60)$ , $(18, 70)$ , $(22, 90)$ , $(25, 120)$ , $(28, 130)$ , $(30, 150)$ , $(32, 160)$ , $(35, 180)$ .
(a)
On the grid, plot the points and draw a line of best fit.
[3 marks]
(b)
Describe the correlation.
[1 mark]
Answer
(c)
Use your line to estimate the mass of a fish $26$ cm long.
[2 marks]
Answer $\dots$ g
Total for D2: 6 marks
D3
The graph shows the rainfall and the umbrellas a shop sold on $7$ days, with a line of best fit.
(a)
Estimate the umbrellas sold on a day with $12$ mm of rain.
[1 mark]
Answer
(b)
On another day $14$ mm of rain fell and $24$ umbrellas were sold. How many fewer is that than the line predicts?
[2 marks]
Answer
Total for D3: 3 marks
D4
Raj says, "The line shows that a $40$ -month-old phone has a battery life of $0$ hours."
The graph shows the age and battery life of $12$ phones, with a line of best fit.
(a)
Describe the correlation.
[1 mark]
Answer
(b)
Estimate the battery life of a $10$ -month-old phone, and the age of a phone whose battery lasts $12$ hours.
[2 marks]
Answer $\dots$ hours; $\dots$ months
(c)
Explain why Raj should not trust this.
[2 marks]
Total for D4: 5 marks

Extension

Stretch

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

E1
A good line of best fit passes through the mean point: (the mean of the $x$ values, the mean of the $y$ values). For the data in the table, a line of best fit also passes through $(0, 8)$ . Estimate $y$ when $x = 9$ , and $x$ when $y = 18$ .
[5 marks]
Hint 1 · What to try
Work out the mean of the $x$ values and the mean of the $y$ values. That point is on the line.
Hint 2 · The first line
The mean point is $(6, 28)$ . From $(0, 8)$ the line goes up $20$ while it goes across $6$ .
Hint 3 · The full method
That is up $10$ for every $3$ across. At $x = 9$ : $8 + 30 = 38$ . For $y = 18$ , go up $10$ from $8$ : across $3$ .
Answer $y = \dots$ , $x = \dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can plot a scatter graph from a table.
I can draw a line of best fit and say if a line is a good one.
I can use a line of best fit to estimate a value.
I can say when an estimate from a line is not reliable.

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