Generating Bivariate Datasets

Suppose we had a set of shapes and two random variables:

• C - that took a shape and returned the number of corners

• E - that took a shape and return the number of edges

If we choose a shape and apply both random variables, we get a pair of numbers:

If we randomly choose a sequence of shapes and apply both random variables, we get a sequence of pairs of numbers:

We can refer to the dataset as and each data point as where represents the place of that data point in the sequence, so for example:

Creating Two-Way Tables

Suppose we surveyed people about:

• Whether or not they like coriander

• Whether they prefer Soccer or Basketball

Suppose we had the following results

• 28 people like coriander and prefer Soccer

• 32 people like coriander and prefer Basketball

• 27 people don’t like coriander and prefer Soccer

• 13 people don’t like coriander and prefer Basketball

We can create a frequency distribution in a two-way table:

Often we also add an extra row and column for sums:

By taking the sum along rows and columns we can obtain more information. From above we can see that:

• 60 people like coriander

• 40 people don’t like coriander

• 55 people prefer Soccer

• 45 people prefer Basketball

• 100 people were surveyed in total

Plotting Repeated Data Points

Suppose we had the dataset:

We can see there is a repeated data point:

One approach we can take to show this on a scatterplot is to use different colours:

If we can’t use different colours, we can instead use different shapes. Either way, it is important to always have a legend with our plot.