For particular situations, only one quadrant of the Cartesian coordinate plane is required to represent a set of data. In these situations, the other quadrants are omitted.

To interpret a graph, it is important to understand what each axis represents and the relationship between them. Identify the variables and/or read the description and the units on both the horizontal and vertical axes to understand the relationship between the two.

The scale and related interval size for each axis are also important to note when interpreting a graph. The horizontal axis scale and interval size can, and often do, differ from the vertical axis scale and interval size because each axis represents something different.

Scale
the range of values noted on each axis, where the length of each axis is divided into identically-sized intervals


In Example 1, the y-axis has a scale of 0% to 100% and is divided into 5% intervals. The x-axis has a scale of 0 minutes to 180 minutes and is divided into 15 minute intervals.

Example 1

The data represented in the graph was collected from five students who volunteered for a study investigating the relationship between exam results and study time.

What information is represented on the horizontal and vertical axes?

The horizontal axis represents study time, in minutes, and the vertical axis represents the exam results, in percentages.

Why is it important for graphs to be properly labelled with a title and descriptive axes?

Without a title and axes descriptions, a graph is nothing more than a pictorial representation of a set of ordered pairs. Proper labels, including units, give the graph context which enables the reader to draw conclusions about the data shown.

Write a conclusion about the relationship between exam results and study time shown in the graph.

As study time increases exam results improve.