Unit 8 Section 3 : Plotting Scatter Diagrams

In this section we review plotting scatter diagrams and discuss the different types of correlation that you can expect to see on these diagrams.

Strong positive correlation between x and y. The points lie close to a straight line with
y increasing as x increases.

Weak, positive correlation between x and y. The trend shown is that
y increases as x increases
but the points are not close to a straight line.

No correlation between x and y; the points are distributed randomly on the graph.

Weak, negative correlation between x and y. The trend shown is that
y decreases as x increases
but the points do not lie close to a straight line.

Strong, negative correlation. The points lie close to a straight line, with
y decreasing as x increases.

If the points plotted were all on a straight line we would have perfect correlation, but it could be positive or negative as shown in the diagrams above.

Example 1

The following table lists values of x and y.

x 2 3 5 6 9 11 12 15
y 10 7 8 5 6 2 5 2
(a)

Use the data to draw a scatter graph.

(b)

Describe the type of correlation that you observe.

It shows weak, negative correlation.

Example 2

What sort of correlation would you expect to find between:

(a)

a person's age and their house number,

No correlation, because these two quantities are not linked in any way.
(b)

a child's age and their height,

Positive correlation, because children get taller as they get older.
(c)

an adult's age and their height ?

No correlation, because the height of adults does not change with their age.

Exercises

Question 1

Consider the following scatter graphs:

(a) Which graph shows strong correlation?
(b) Which graphs show positive correlation?
(c) Which graph shows negative correlation?
(d) Which graph shows a weak, positive correlation?
Question 2

The following table lists values of x and y.

x 2 4 6 7 8 9 10 11 12
y 3 5 8 5 9 6 9 9 11
(a)

Plot a scatter graph for this data.

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(b)

Describe the correlation between x and y.

Question 3

Complete the table below for 10 people in your class.

House Number
Day of Month of Birthday
(a)

Plot a scatter graph for your data.

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(b)

Describe the type of correlation that there is between these two quantities.

Question 4

A driver keeps a record of the distance travelled and the amount of fuel in his tank on a long journey.

Distance Travelled (km) 050100150200250300
Fuel in Tank (litres) 80736761524637
(a)

Illustrate this data with a scatter plot.

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(b)

Describe the type of correlation that is present.

Question 5

What type of correlation would you expect to find between each of the following quantities:

(a)

Age and pocket money

(b)

IQ and height,

(c)

Price of house and number of bedrooms,

Possibly strong positive correlation in a single, smallish geographical area. For wider areas with greater mix of housing, little or no correlation.
(d)

Person's height and shoe size ?

Question 6

In a class 10 pupils took a Science test and an English test. Their scores are listed in the following table:

Pupil ABCDEFGHIJ
English Score 210184971819310
Science Score 181263112041772
(a)

Draw a scatter graph for this data.

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(b)

Describe the correlation between the two scores.

Question 7

Chris carries out an experiment in which he measure the extension of a spring when he hangs different masses on it. The following table lists his results:

Mass (grams) 2050100120200
Extension (cm) 1.23.067.212
(a)

Draw a scatter graph for this data.

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(b)

Describe the correlation between the mass and the extension.

Perfect positive correlation
Question 8

Every day Peter picks the ripe tomatoes in his greenhouse. He keeps a record of their mass and the number that he picks. His results are listed in the following table:

Number of Tomatoes Picked 13258674
Total Mass (grams) 4018060270390220420210
(a)

Draw a scatter graph for this data.

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(b)

Describe the correlation between the number of tomatoes picked and their total mass.

Question 9

A competition has 3 different games.

(a)

Jeff plays 2 of the games.

Game A Game B Game C
Score 62 53

To win, Jeff needs a mean score of 60. How many points does he need to score in Game C?

Mean score ≥ 60 ⇒ total score ≥ 3 × 60 = 180
⇒ score in Game C ≥ 180 – 62 – 53 = 65;
so he needs to score at least 65 in Game C.
(b)

Imran and Nia play the 3 games. Their scores have the same mean.
The range of Imran's score is twice the range of Nia's scores.
Fill in the missing scores in the following table.

Imran's Scores 40
Nia's Scores 35 40 45
The scatter diagrams show the scores of everyone who plays all 3 games.
(c)

Look at the scatter diagrams. Choose a statement which most closely describes the relationship between the games.

Game A and Game B:

Game A and Game C:

(d)

What can you tell about the relationship between the scores on Game B and the scores on Game C? Write down the statement below which most closely describes the relationship.

Game B and Game C: