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Scatter diagrams show the relationship between two sets of variables. By looking at the diagram you can see whether there is a link between variables. Where there is a link it is called correlation.
The English and Maths results of ten classmates are shown in the table below:
Name | Sal | Kim | Bill | Tom | Gita | Alex | Bev | Ken | Alan | Jo |
---|---|---|---|---|---|---|---|---|---|---|
Maths mark | 20 | 71 | 60 | 52 | 80 | 32 | 47 | 90 | 49 | 80 |
English mark | 30 | 80 | 65 | 50 | 81 | 38 | 40 | 87 | 55 | 70 |
To see whether there is a correlation between the Maths and English marks, you could plot a scatter diagram.
The Maths mark is on the horizontal scale and the corresponding English mark on the vertical scale.
Bill's Maths mark was 60 and his English mark was 65, so his results are represented by the orange point at coordinates (60, 65).
In the scatter diagram above, whose mark does the small red cross represent?
The co-ordinates of the cross are (80, 70).
Therefore, the Maths mark is 80 and the English mark 70.
The highlighted cross represents Jo's marks.
You can see that all the points representing Maths marks and English marks lie approximately along a straight line. This shows that there is a correlation between these two variables.
The table below shows the correlations that you can deduce from different patterns of scatter.
Positive correlation | Negative correlation | No correlation |
---|---|---|
The points lie close to a straight line, which has a positive gradient. |
The points lie close to a straight line, which has a negative gradient. |
There is no pattern to the points. |
Would you expect there to be positive correlation, negative correlation, or no correlation between the following pairs of variables:
a) Temperature and sales of ice-cream
b) Height and intelligence
a) As temperature increases, the sales of ice-cream are also likely to increase. Therefore, there is likely to be positive correlation.
b) It is unlikely that there is a connection between height and intelligence. Therefore, there is no correlation.
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