Module 2 (M2) - Handling data - Scatter graphs

Scatter graphs

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

Example

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

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.

Graphs can either 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.

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

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

Scatter plots often have a pattern. We call a data point an outlier if it doesn't fit the pattern.

The scatter graph below shows data for students on a hiking trip.

Each student is carrying a backpack and each point on the graph represents a student.

Two of the points don't fit the pattern very well.

These points have been labeled Brad and Sharon, which are the names of the students they represent.

Sharon could be considered an outlier because she is carrying a much heavier backpack than the pattern predicts.

Brad could be considered an outlier because he is carrying a much lighter backpack than the pattern predicts.

A line of best fit is a sensible line that goes as centrally as possible through the coordinates plotted. It should also follow the same steepness of the crosses.

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 3 mm of rainfall? What if there was 10 mm of rainfall?

To estimate the number sold for 3 mm of rainfall, we use a process called interpolation. The value of 3 mm 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. Use this line to estimate the number of umbrellas sold by going across from 3 mm and then down to find the number of umbrellas.

An estimated 20 umbrellas would be sold if there was 3 mm of rainfall.

If there was 10 mm 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 80 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 10 mm 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 10 mm, so the value of 80 umbrellas is not a reliable estimate.