Scatter graphs

Scatter graphs are a good way of displaying two sets of data to see if there is a correlation, or connection.

Types of correlation

Graphs can have: positive correlation; negative correlation; or no correlation.

Positive correlation means as one variable increases, so does the other variable. They have a positive connection.

Temperature vs ice creams sold graph

Negative correlation means as one variable increases, the other variable decreases. They have a negative connection.

Graph showing negative correlation between number of coats sold and rising temperatures

No correlation means there is no connection between the two variables.

Graph showing no correlation between house number and a person's IQ

Example

The number of umbrellas sold and the rainfall (mm) on 9 days is shown on the scatter graph and in the table.

A scatter graph that plots how many umbrellas are sold in comparison to accumulated rainfall. The plot points show a positive correlation ie, at 2mm of rain 10 are sold and at 4mm 25 are sold.
Umbrellas sold11025013247815
Rainfall (mm)324005611

The graph shows that there is a positive correlation between the number of umbrellas sold and the amount of rainfall. On days with higher rainfall, there were a larger number of umbrellas sold.

However, it is important to remember that correlation does not imply causation. If data plotted on a scatter graph shows correlation, we cannot assume that the increase in one of the sets of data caused the increase or decrease in the other set of data – it might be coincidence or there may be some other cause that the two sets of data are related to.

Lines of best fit

A line of best fit is a sensible straight line that goes as centrally as possible through the coordinates plotted. It should show the general trend of the relationship between the two sets of data.

Positive and negative lines on a single  graph

The line of best fit for the scatter graph would look like this:

A scatter graph that plots how many umbrellas are sold in comparison to accumulated rainfall. A line of best fit passes as centrally as possible through the points plotted.

Interpolation and extrapolation

From the diagram above, we can estimate how many umbrellas would be sold for different amounts of rainfall. For example, how many umbrellas would be sold if there was 3mm of rainfall? What if there was 10mm of rainfall?

To estimate the number sold for 3mm of rainfall, we use a process called interpolation. The value of 3mm is within the range of data values that were used to draw the scatter graph.

Find where 3 mm of rainfall is on the graph. Draw a line by going across from 3 mm and then down.

A graph estimates umbrellas sold for 3mm of rainfall using interpolation. A vertical line drawn at 3 mm meets the line of best fit in the centre and a line across meets the vertical axis giving 19.

An estimate of 19 umbrellas would be sold if there was 3 mm of rainfall.

If there was 10mm of rainfall, we could extend the graph and the line of best fit to read off the number of umbrellas sold. This gives a value of approximately 64 umbrellas sold.

This process is called extrapolation, because the value we are using is outside the range of data used to draw the scatter graph. Since 10mm is much higher than the highest rainfall recorded, we cannot assume that the line of best fit would still follow the pattern when the rainfall is 10mm, so the value of 64 umbrellas is not a reliable estimate.

A graph estimates umbrellas sold for 10mm of rainfall using extrapolation. A vertical line drawn at 10 mm meets the extended line of best fit and a line across meets the vertical axis giving 64.