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Representing data

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# Scatter diagrams *

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.

### Example

The English and Maths results of ten classmates are shown in the table below:

 Name Maths mark English mark Sal Kim Bill Tom Gita Alex Bev Ken Alan Jo 20 71 60 52 80 32 47 90 49 80 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).

### Sample scatter diagram

The lines indicate the points from axis to coordinate

Question

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.
This shows that as one variable increases the other increases.

The points lie close to a straight line, which has a negative gradient.
This shows that as one variable increases, the other decreases.

There is no pattern to the points.
This shows that there is no connection between the two variables.

Question

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