1. Mathematics
Scatter Graphs

2. 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.

3. 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.

4. 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.

5. 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.

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

7. Which of these graphs shows positive correlation?
Click on the button beneath the graph you choose. 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
Well done!
Uphill trend = positive correlation
Click here to continue 

8. Which of these graphs shows positive correlation?
Click on the button beneath the graph you choose. 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
OOPs! Positive correlation = uphill trend  middle graph
Click here to continue 

9. 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).

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

11. Which of these graphs shows negative correlation?
Click on the button beneath the graph you choose. 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
Well done!
Downhill trend = negative correlation
Click here to continue 

12. Which of these graphs shows negative correlation?
Click on the button beneath the graph you choose. 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
OOPs! Negative correlation = downhill trend  graph on the right
Click here to continue 

13. 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.

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

15. Which of these graphs shows NO correlation?
Click on the button beneath the graph you choose. 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
Well done! Scattered plots = graph on the right  No correlation
Click here to continue 

16. Which of these graphs shows NO correlation?
Click on the button beneath the graph you choose. 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
OOPs! No correlation = high & low plots everywhere  Graph on right
Click here to continue 

17. 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!

18. Check 1
What sort of correlation would you expect between temperature and ice cream sales?
Positive
Correlation
Negative No

19. Check 1
What sort of correlation would you expect between temperature and ice cream sales?
Positive
Correlation
Negative No
Well done!
As the temperature increases, you’d expect to sell more ice creams so both variables increase together  Positive Correlation
Click here to continue 

20. Check 1
What sort of correlation would you expect between temperature and ice cream sales?
Positive
Correlation
Negative No
OOPS!
As the temperature increases, you’d expect to sell more ice creams so both variables increase together  Positive Correlation
Click here to continue 

21. Check 2
What sort of correlation would you expect between speed and the time taken to reach your destination?
Positive
Correlation
Negative No

22. Check 2
What sort of correlation would you expect between speed and the time taken to reach your destination?
Positive
Correlation
Negative No
Well done!
As the speed increases, it takes less time to get there, i.e. more speed less time  Negative Correlation
Click here to continue 

23. Check 2
What sort of correlation would you expect between speed and the time taken to reach your destination?
Positive
Correlation
Negative No
OOPS!
As the speed increases, it takes less time to get there, i.e. more speed less time  Negative Correlation
Click here to continue 

24. Check 3
Up to the age of 18, what sort of correlation would you expect between age and height?
Positive
Correlation
Negative No

25. Check 3
Up to the age of 18, what sort of correlation would you expect between age and height?
Positive
Correlation
Negative No
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
Click here to continue 

26. Check 3
Up to the age of 18, what sort of correlation would you expect between age and height?
Positive
Correlation
Negative No
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
Click here to continue 

27. Check 4
What sort of correlation would you expect between your house number and your age?
Positive
Correlation
Negative No

28. Check 4
What sort of correlation would you expect between your house number and your age?
Positive
Correlation
Negative No
Well done!
You wouldn’t expect any connection between house number and age 
No Correlation
Click here to continue 

29. Check 4
What sort of correlation would you expect between your house number and your age?
Positive
Correlation
Negative No
OOPS!
You wouldn’t expect any connection between house number and age 
No Correlation
Click here to continue 

30. Check 5
What sort of correlation would you expect between temperature and the sales of soup?
Positive
Correlation
Negative No

31. Check 5
What sort of correlation would you expect between temperature and the sales of soup?
Positive
Correlation
Negative No
Well done!
As the temperature drops, you’d expect to sell more (hot) soup, i.e. less temperature, more soup sold  Negative Correlation
Click here to continue 

32. Check 5
What sort of correlation would you expect between temperature and the sales of soup?
Positive
Correlation
Negative No
OOPS!
As the temperature drops, you’d expect to sell more (hot) soup, i.e. less temperature, more soup sold  Negative Correlation
Click here to continue 

33. 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 5 2
French 3

34. Plotting a scatter graph - Example
Label and number the axes
Plot each pairing
Maths 7 6 8 4 9 5 2
French 3 10 8 6 4 2
Maths
French x x x x x x x x x x

35. Plotting a scatter graph - Example
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) 10 8 6 4 2
Maths
French x x x x x x x x x x

36. 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.

37. 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).

38. 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…

39. Plotting a scatter graph - Example 10 8 6 4 2
Maths
French x x x x x x x x x x
This IS a good line of best fit.
Right direction – 3/4 crosses above and below!
This is not a good line of best fit.
It’s going in the wrong direction and it’s too short!
This is not a good line of best fit.
It’s got more plots above than below the line

40. 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?

41. Plotting a scatter graph - Example 10 8 6 4 2
Maths
French x x x x x x x x x x
Q2. Someone getting 8 in French, would probably get…
10 in maths!
Q1. Someone getting 3 in maths would probably get… 3 in French too!
Q3. The first estimate is more reliable than the second
because it is interpolated rather than extrapolated.

42. 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:
Online HW:
Work through the MyMaths lesson and its online homework called Line of Beat Fit which can be found at:
Lesson:
Online HW:
Continued on the next slide…

43. 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.