# Australian Bureau of Statistics

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 Understanding statistics

Module 3: Interpreting Data

5.3 Scatter plots

5.3.7 What happened to frequency?

Almost every graph we have discussed had an axis for frequency. But the scatterplot does not! Why not?

To answer that question, we will consider a data set which measures the strength and diameter of wool fibres taken from some 150 Romney sheep in New Zealand (but you won't be referred to the original data!).

Below are two views of the scatterplot for the data and you can see that there is a strong positive association between the variable “diameter” and the variable “strength”. The first plot is in normal two dimensional mode but you will notice that some data crosses are heavy (bold) – because there is more than one value in that space. The second diagram has been generated by computer to show a 3D perspective.

 2D representation 3D representation

In the 3D view a third axis emerges (vertical) which in pure mathematics is usually called the z-axis. We can use it for frequency.

The following representation is the same data, but uses columns to represent frequency. The heavy (bold) crosses will have columns of height (frequency) with values 2 and/or greater because there is more than one data point in that space. The pale crosses will all have height (frequency) of exactly 1 (unity).

You are not expected to produce 3D simulated graphs like this, and it is always a challenge to draw a 3D diagram on 2D paper! But now you have a complete understanding of the scatterplot!