Describing categorical and discrete populations

Since probabilities can be treated as population proportions, they can be displayed graphically in the same way that sample proportions are displayed — with bar charts.

Alternative interpretation of bar charts

An alternative interpretation of these bar charts comes from the Law of Large Numbers. If we imagine repeating the data collection to increase the sample size indefinitely, the Law of Large Numbers states that the sample proportions in the different categories will eventually stabilise at the underlying population proportions (probabilities).

Examples

The 'infinite-sample' barchart gives probabilities that describe the population distribution.