GCSE Statistics · Higher · Chapter 10: Correlation and regression · Lesson 1

Scatter diagrams and correlation

About 50 minutesCalculator allowed41 marks

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Date

Do Now

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

A1
Needed today
$M (- 3, 1)$ is the midpoint of $A (0, 4)$ and $B$ . Find the coordinates of $B$ .
[2 marks]
Answer
A2
From chapter 5
In a histogram of the journey times, in minutes, of some commuters, the class $10 < t \leq 25$ has frequency $10$ and is drawn as a bar $3$ cm tall. The class $25 < t \leq 55$ has frequency $32$ . How tall should its bar be?
[2 marks]
Answer
A3
Last lesson
A gym's new members in Q2 of three years were $71$ , $92$ , $108$ . The trend values for those quarters were $78$ , $94$ , $111$ , and the mean of all twelve quarters was $91$ . Work out the mean seasonal variation for Q2, to 1 decimal place.
[2 marks]
Answer
A4
Maths skill
7 numbers have a mean of $13$ . 6 of the numbers are $2, 10, 28, 8, 6, 8$ . Find the other number.
[2 marks]
Answer

Examples, then your turn

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

Example 1

A gardener records the amount of fertiliser each plant is given and the height it grows to. Which is the explanatory variable? Which axis should it go on?

Hint Ask which one is changed, and which one is expected to change because of it.

B1
A family records the outside temperature each day and the amount of gas used to heat their house that day. Write down the explanatory variable and give a reason. Which axis of a scatter diagram should it go on?
[2 marks]

Example 2

The scatter diagram shows the hours of sunshine and the number of ice creams sold at a beach kiosk on 8 days. Describe the correlation and interpret it in context.

Hint Say the type of correlation, then say what it means using the words in the question.

B2
The scatter diagram shows the age and the value of 8 cars of the same model. Describe the correlation and interpret it in context.
[2 marks]

Example 3

The scatter diagram shows the maths and science marks of 9 students. One student's marks do not fit the pattern. Write down this student's marks and give a possible reason.

Hint Look for the point far from the others. Read across and up to the axes.

B3
The scatter diagram shows the age and the height of 9 trees. Write down the age and the height of the tree that does not fit the pattern. Give a possible reason.
[2 marks]

Example 4

For children aged 5 to 11 there is positive correlation between shoe size and reading score. Explain why this does not mean that bigger feet make a child read better.

Hint Think of something that makes both of them go up.

B4
In a survey of 12 towns, there is strong positive correlation between the number of cafés in a town and the number of road accidents each year. A councillor says that the cafés cause the accidents. Explain why the councillor may be wrong.
[2 marks]

Practice

C1
The scatter diagram shows the hours of television watched and of exercise taken by 8 people last week. Two more people watched $7$ and $12$ hours and exercised for $5$ and $7$ hours. Plot these two points. Describe the strength and the type of correlation for all 10 people.
[4 marks]
Answer $\dots\dots\dots\dots$ correlation
C2
Amy recorded the height and the mass of 9 men. She thinks the point at $176$ cm should be removed. Is she right? Give a reason.
[2 marks]

C3
Write down the type of correlation you would expect for each pair: positive, negative or none. (i) The hours a waiter works and his pay. (ii) The outside temperature and the number of coats a shop sells. (iii) A person's house number and their age.
[3 marks]
Answer(i) $\dots\dots$ (ii) $\dots\dots$ (iii) $\dots\dots$
C4
A vet records the age and the mass of 20 dogs of one breed. Give two reasons why a scatter diagram is a suitable way to show these data.
[2 marks]

Exam-style questions

D1
Jo wants to find out if students who spend more time on social media sleep for fewer hours. This is her plan.
Step 1: ask the 8 students in her friendship group how many hours they spent on social media yesterday and how many hours they slept last night.
Step 2: draw a scatter diagram with hours of sleep on the horizontal axis.
Step 3: if the points show negative correlation, conclude that social media makes students sleep less.
Assess Jo's plan. Comment on each part of it.
[4 marks]

D2
A coach records the number of hours 12 students train each week and the time each student takes to run 400 m.
(a)
Describe the correlation. Interpret it in the context of the question.
[2 marks]
(b)
One student does not fit the pattern. Write down this student's hours of training and time. The coach decides not to remove this result. Give a reason why.
[2 marks]
(c)
Work out the percentage of these students who ran 400 m in less than $75$ seconds. Give your answer to 1 decimal place.
[2 marks]
Answer
Total for D2: 6 marks

Extension

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

E1
The table shows the population, the number of libraries and the number of cafés in six towns. The numbers of libraries and cafés show strong positive correlation. Nadia says, "Libraries bring cafés to a town."
Work out the number of libraries and the number of cafés for every $10000$ people in each town. Use your answers to comment on Nadia's claim.
[4 marks]
Hint 1 · What to try
Divide each count by the number of $10000$ s of people in that town.
Hint 2 · The first line
Town B has $2$ lots of $10000$ people, so $5 \div 2 = 2.5$ libraries for every $10000$ people.
Hint 3 · The full method
Libraries per $10000$ : $1, 2.5, 1.5, 1, 2, 1$ . Cafés per $10000$ : $3, 3, 6, 5, 7, 5$ . Do these go up together?

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can describe correlation in context.
I can choose the explanatory variable and spot a point that does not fit.
I can explain why correlation does not show cause.

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