Patterns and exceptions
The reasons why graphs are so important is that they provide a way to visualise data that is easy to understand. People can often identify trends and patterns when looking at a graph that they would not be able to see when looking at a table of numbers.
It is important that you have the ability to identify patterns and trends in graphical data and understand and apply key mathematical terms in your answers to any questions.
In mathematics, there are three key ways that we can describe a trend in a graph as is shown in these three scatter graphs:
Positive correlation – as one variable increases so does the other.
Negative correlation – as one variable increases the other decreases.
No correlation – one variable increase has no impact on the other.
In addition to being able to state the correlation, we also have to be able to describe and explain the shape of a graph.
Straight line
This means the relationship between the two variables is linear. The steepness of the line is the gradient. The gradient tells us the rate of change – how quickly one variable is changing compared to the other.
A steeper gradient means a larger rate of change.
Curve up
This curve tells us that the relationship is not linear and that the rate of change is increasing.
Curve down
Again, this curve tells us that the relationship between the two variables on the axis is not linear. However, this time the rate of change is decreasing.
