MATHEMATICS Scatter Graphs. Lesson Objectives The aim of this powerpoint is to help you to learn…...

MATHEMATICSScatter Graphs

Lesson Objectives

•The aim of this powerpoint is to help you to learn…

• how to plot a scatter graph• how to recognise correlation• how to draw and use lines of best fit.

Scatter Graphs

• Scatter graphs are used to see whether there is a link or relationship (known as correlation) between 2 sets of numeric data (aka bivariate data)

• The pairs of data values are plotted like co-ordinates with small crosses.

• Once all the plots are in place, you look for a pattern in the data. This pattern is called correlation.

• If there is correlation, you can draw a line of best fit.

Scatter Graphs – subject differences

• In science a line of best fit can be curved but in maths at KS3 and KS4, lines of best fit MUST be one straight line.

• In maths, you can draw a line of best fit ‘by eye’. However in statistics, you must first plot the *double mean point and the line of best fit MUST go through this point!

*Find the mean average of the first set of data, find the mean average of the second set of data, plot these pair of averages as the double mean point using a dot (not a cross) in order to distinguish it from the other plots.

Positive Correlation

• If the pattern of the plots is generally going uphill (as you look from left to right), then there is positive correlation.

• The closer these plots are to being in a straight line, the ‘stronger’ the correlation.

• Positive correlation indicates that both variables are doing the SAME thing, i.e. as one variable increases then so does the other variable.

• Which of these graphs shows positive correlation?• Click on the button beneath the graph you choose.

xx x x x x x

x x x x x x x x x

x x x x x x x x x x x x


xx x x x x x

x x x x x x x x x


Well done! Uphill trend = positive correlation

Click here to continue


xx x x x x x

x x x x x x x x x


OOPs! Positive correlation = uphill trend middle graph


Negative Correlation

• If the pattern of the plots is generally going downhill (as you look from left to right), then there is negative correlation.

• The closer these plots are to being in a straight line, the ‘stronger’ the correlation.

• Negative correlation indicates that the two variables are doing the opposite to each other, i.e. as one variable increases the other variable decreases (and vice versa).

• Which of these graphs shows negative correlation?• Click on the button beneath the graph you choose.

xx x x x x x

x x x x x x x x x



xx x x x x x

x x x x x x x x x


Well done! Downhill trend = negative correlation



xx x x x x x

x x x x x x x x x


OOPs! Negative correlation = downhill trend graph on the right


No Correlation

• If there is NO general pattern (uphill or downhill) to the plots, i.e. there are some high and low plots all over the place, then there is NO correlation.

• This means that the two variables are not linked and have no effect on each other.

• You can NOT draw a line of best fit if there is no correlation.

• Which of these graphs shows NO correlation?• Click on the button beneath the graph you choose.

xx x x x x x

x x x x x x x x x



xx x x x x x

x x x x x x x x x


Well done! Scattered plots = graph on the right No correlation



xx x x x x x

x x x x x x x x x


OOPs! No correlation = high & low plots everywhere Graph on right


Quick Check• For each of the following click on the button that best

describes the correlation between the two variables described.

• Remember…

• Positive correlation: Both variables increase or decrease at the same time

• Negative correlation: As one variable increases, the other decreases (and vice versa)

• No correlation: There is no link between the variables – one does not affect the other!

Check 1

• What sort of correlation would you expect between temperature and ice cream sales?

Positive

Correlation

Negative

Correlation

No

Correlation

Check 1


Positive

Correlation

Negative

Correlation

No

Correlation

Well done!As the temperature increases, you’d expect to sell more ice creams so both variables increase together Positive Correlation


Check 1


Positive

Correlation

Negative

Correlation

No

Correlation

OOPS!As the temperature increases, you’d expect to sell more ice creams so both variables increase together Positive Correlation


Check 2

• What sort of correlation would you expect between speed and the time taken to reach your destination?

Positive

Correlation

Negative

Correlation

No

Correlation

Check 2


Positive

Correlation

Negative

Correlation

No

Correlation

Well done!As the speed increases, it takes less time to get there, i.e. more speed less time Negative Correlation


Check 2


Positive

Correlation

Negative

Correlation

No

Correlation

OOPS!As the speed increases, it takes less time to get there, i.e. more speed less time Negative Correlation


Check 3

• Up to the age of 18, what sort of correlation would you expect between age and height?

Positive

Correlation

Negative

Correlation

No

Correlation

Check 3


Positive

Correlation

Negative

Correlation

No

Correlation

Well done!From when you are born up to about 18, as you get older you get taller, i.e. more age, more height Positive Correlation


Check 3


Positive

Correlation

Negative

Correlation

No

Correlation

OOPS!From when you are born up to about 18, as you get older you get taller, i.e. more age, more height Positive Correlation


Check 4

• What sort of correlation would you expect between your house number and your age?

Positive

Correlation

Negative

Correlation

No

Correlation

Check 4


Positive

Correlation

Negative

Correlation

No

Correlation

Well done!You wouldn’t expect any connection between house number and age No Correlation


Check 4


Positive

Correlation

Negative

Correlation

No

Correlation

OOPS!You wouldn’t expect any connection between house number and age No Correlation


Check 5

• What sort of correlation would you expect between temperature and the sales of soup?

Positive

Correlation

Negative

Correlation

No

Correlation

Check 5


Positive

Correlation

Negative

Correlation

No

Correlation

Well done!As the temperature drops, you’d expect to sell more (hot) soup, i.e. less temperature, more soup sold Negative Correlation


Check 5


Positive

Correlation

Negative

Correlation

No

Correlation

OOPS!As the temperature drops, you’d expect to sell more (hot) soup, i.e. less temperature, more soup sold Negative Correlation


Plotting a scatter graph - Example

• Ella says that people who are better at maths are also better at languages.

• To test this, she gets details of 10 of her classmate’s scores for their last maths test and their last French test.

• Here is the data:

Maths 7 6 8 4 9 7 5 4 2 7

French 6 6 5 4 4 8 5 3 3 5


• Label and number the axes• Plot each pairing

Maths 7 6 8 4 9 7 5 4 2 7

French 6 6 5 4 7 8 5 3 3 5

x

x x

x

xx

xx

x x

0 2 4 6 8 10

10

8

6

4

2

Maths

Fre

nch


• On the left, plots tend to be lower than on the right• There is an ‘uphill’ trend = positive correlation• Ella appears to be correct (higher Maths higher French)

x

x x

x

xx

xx

x x

0 2 4 6 8 10

10

8

6

4

2

Maths

Fre

nch

Lines of Best Fit

• Lines of best fit can only be drawn IF there IS correlation (whether positive or negative).

• At KS3 and KS4 in mathematics, these lines can be drawn ‘by eye’.

• They should be one STRAIGHT line in the direction of the pattern of plots.

• They should pass through, or be as close to, as many plots as possible and have about the same number of crosses above the line as below it.

Using Lines of Best Fit

• Once drawn, they can be used to estimate values for one of the variables using a value for the other variable.

• Draw appropriate lines to and from the line of best fit to show where your estimate comes from.

• Remember that interpolation (an estimate using part of the line that

falls between known plots) is more accurate/reliable than extrapolation (an estimate using part of the line that starts before the first plot or comes after the last plot).

Lines of Best Fit - Example

• Let’s use Ella’s scatter graph which shows the link between Maths and French.

• Before using it for estimates we need to draw an accurate line of best fit…


• This is not a good line of best fit.• It’s going in the wrong direction and it’s too short!

x

x x

x

xx

xx

x x

0 2 4 6 8 10

10

8

6

4

2

Maths

Fre

nch

• This is not a good line of best fit.• It’s got more plots above than below the line

• This IS a good line of best fit.• Right direction – 3/4 crosses above and below!

Lines of Best Fit - Example

• Let’s use our scatter graph and line of best fit…

Q1. Estimate the French score for someone getting a

score of 3 for Maths.

Q2. Estimate the Maths score for someone getting a

score of for French.

Q3. Which of these estimates is more reliable? Why?


Q1. Someone getting 3 in maths would probably get…

3 in French too!

x

x x

x

xx

xx

x x

0 2 4 6 8 10

10

8

6

4

2

Maths

Fre

nch

Q3. The first estimate is more reliable than the second

because it is interpolated rather than extrapolated.

Q2. Someone getting 8 in French, would probably get…

10 in maths!

What next?• Print out and read through the notes called Data10.

• Work through the MyMaths lesson and its online homework called Scatter Graphs which can be found at:

• Lesson: http://app.mymaths.co.uk/358-resource/scatter-graphs • Online HW: http://app.mymaths.co.uk/358-homework/scatter-graphs

• Work through the MyMaths lesson and its online homework called Line of Beat Fit which can be found at:

• Lesson: http://app.mymaths.co.uk/359-resource/line-of-best-fit • Online HW: http://app.mymaths.co.uk/359-homework/line-of-best-fit

Continued on the next slide…

http://app.mymaths.co.uk/358-resource/scatter-graphs



http://app.mymaths.co.uk/358-homework/scatter-graphs

http://app.mymaths.co.uk/358-homework/scatter-graphs

http://app.mymaths.co.uk/359-resource/line-of-best-fit



http://app.mymaths.co.uk/359-homework/line-of-best-fit



What next? (cont’d)• Answer the tasks that appear throughout the Data10 notes.

• Copy, save and complete the worksheets: Scatter-S1.xlsx, LoBF-S1.xlsx and ScatU-S1.xlsx

• There are other data reps such as stem & leaf diagrams, which will be dealt with in a different module of work, as well as box (and whisker) plots, cumulative frequency curves and histograms, which are dealt with at KS4 at Higher tier.

• You should now REVISE the whole of this module of work and then undertake the assessment.

MATHEMATICS Scatter Graphs. Lesson Objectives The aim of this powerpoint is to help you to learn…...

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