Scatter diagrams - plotting and reading

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Scatter diagrams show the relationship between two variables. By looking at the diagram you can see whether there is a link between variables. If there is a link it is called correlation.

Reading scatter diagrams

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

SalKimBillTomGitaAlexBevKenAlanJo
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 marks and the English marks, you can 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 purple point at coordinates ({60},~{65}).

Scatter diagram

Diagram showing Maths and English marks.

Question
Scatter diagram

In the scatter diagram above, whose marks are represented by the small purple cross?

The coordinates of the cross are ({80},~{70}).

Therefore, the Maths mark is {80} and the English mark is {70}.

So the small purple cross represents Jo's marks.

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Notice 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 diagrams below show the correlations that you can deduce from different patterns of scatter.

Positive correlation

The points lie close to a straight line, which has a positive gradient.

This shows that as one variable increases the other increases.

Positive correlation

Negative correlation

The points lie close to a straight line, which has a negative gradient.

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

Negative correlation

No correlation

The points do not lie close to any straight line.

This shows that there is no connection between the two variables.

No correlation
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

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.