ScattergramsA scattergram a type of graph that is used to try to find a relationship between two variables (things)

Here is an example of how the information about AGE and AMOUNT OF MONEY SPENT AT THE WEEKEND is put onto a scattergram.

People were asked:

What is your age?

How much money did you spend this weekend?

Their answers were recorded in a table like this:

I’m 18 and

I spent £25

Age 18 16

Amount 25 10

I’m 16 and I spent

£10

Age 18 16 17 15 18

Amount 25 10 22 8 10

I’m 18 and I

spent £10

I’m 17 and

I spent £22I’m 15

and I

spent £8

Age 18 16 17 15 18 17 19

Amount 25 10 22 8 10 15 30

I’m 17

and I spent £15

I’m 19

and I spent £30

Age x 18 16 17 15 18 17 19

Amount y 25 10 22 8 10 15 30

Age - Amount Spent

05

101520253035

0 5 10 15 20

Age

Am

ou

nt

Sp

en

t

This graph needs to be rescaled.

Age 18 16 17 15 18 17 19

Amount 25 10 22 8 10 15 30

Age - Amount Spent

05

101520253035

12 14 16 18 20

Age

Am

ou

nt

Sp

en

t

This graph is clearer due to a better scale.

This line is called the line of best fit.

If it goes up in this direction, it has a positive correlation.

Age - Amount Spent

05

101520253035

12 14 16 18 20

Age

Am

ou

nt

Sp

en

t

click on hyperlink above

To measure the correlation a value r is calculated which lies between –1 and +1. This is called the correlation coefficient

If all the points lie on a perfect straight line then r equals either +1 or –1.

If the points are totally scattered and there appears to be no line of best fit then r = 0.

Other values of r indicate a degree of correlation – strong, medium or weak.

Types of Correlation

Perfect positive correlation

r = 1

Moderate positive correlation

r = 0.6

Very weak positive correlation

r = 0.1

No correlation

r = 0

Quite strongnegative correlation

r = –0.7

Perfect negative correlation

r = –1

Drawing the line of best fit.

Age - Amount Spent

05

101520253035

12 14 16 18 20

Age

Am

ou

nt

Sp

en

t

The line of best fit must pass through the:

Mean x value and the mean y value

Finding the mean x and y value

Age x 18 16 17 15 18 17 19

Amount y 25 10 22 8 10 15 30

To find the mean x value add up all the ages and divide by how many there are

Total age = 18+16+17+15+18+17+19 = 120

Number of values = 7

Mean Age = 120

17.17

Finding the mean x and y value

Age x 18 16 17 15 18 17 19

Amount y 25 10 22 8 10 15 30

To find the mean y value add up all the money and divide by how many there are

Total age = 25+10+22+8+10+15+30 = 120

Number of values = 7

Mean Age = 120

17.17

Drawing the line of best fit.Age - Amount Spent

0

5

10

15

20

25

30

35

12 14 16 18 20

Age

Am

ou

nt

Sp

en

t

Series1

The line of best fit must pass through the point(17.1, 17.1) The mean x and y values are not usually the same

Drawing the line of best fit.

If the data is plotted using EXCEL then the value of r can be obtained

Using the handout on using Excel follow the stages to plot the scatter diagram and draw the line of best fit with the correlation coefficient r

 

1.Plot these points on a scattergram.

Pupil A B C D E F G H I J K L M

Shoe S. 2 2 3 4 5 7 6 5 6 7 4 3 2

Height 1.3 1.5 1.4 1.4 1.5 1.8 1.7 1.6 1.6 2 1.3 1.5 1.3

a. What type of correlation does the scattergram show between shoe size and height?

b. What can you usually say about the connection between shoe size and height?

Plot these points on a scattergram to show the connection between revision and number of GCSE passes.

Pupil A B C D E F G H I J K L

Hours Rev.

45 67 97 34 5 78 34 12 49 76 89 90

No. GCSE

4 6 9 1 0 5 2 1 5 8 9 10

a. What type of correlation does this showb. Draw a line of best fit onto the scattergram after

having determined the mean x and the mean y value. c. Use this line to estimate how many hours are needed

for 7 GCSE passes.