Describing Line Graphs (6)

Observe the following simple line graph:

This shows simply a series of numbers from zero (0) to one hundred million (100,000,000).

The graph is generated from the numbers in the table below.

You can see that the numbers do not increase in a linear fashion. Each increase is ten times the previous one (apart from 2013/2014). So when we put these figures into a graph with a linear scale most of the values on the Y-axis seem to be close to zero. This is why we sometimes use a logarithmic scale, as in the graph below.

Now we have a straight line and the graph is easier to read and interpret.

But you have to be careful. The line on this graph is perfectly straight only because the series of numbers is a logarithmic one and the Y-axis is a logarithmic scale: most graphs series will not be perfectly logarithmic: they will vary in a logarithmic fashion which means that the data is better presented on a logarithmic scale. And you have to be careful when describing these graphs. Although the line on this graph is straight you cannot say there is a steady increase. The rate of increase changes with time, becoming steeper and steeper very quickly, as you can see from the linear scale.

See Understanding Coronavirus Graphs for an authentic example of the use of a logarithmic scale.

Often, the type of scale is not indicated on the graph so you have to look at the numbers on the axes to decide if the scale is linear or logarithmic.

Again it is very important when interpreting graphs to be aware of how the data is presented. Not only do you have to look at the title, the X and Y axes, the labels and the units, you also need to look at the scale.

The decision to use a particular scale may not always be taken on the basis of the clearest way to present the data. It may be made in order to affect the reader's perception of the data which are presented. So looking at the scale is very important.