1.1.3 Statistical Analysis of Categorical Distributions

Answering Statistical Questions on Categorical Distributions

Mode

• The mode of categorical data refers to the category with the highest frequency.

Note: the mode of a categorical distribution is also known as the modal category, or dominant category

Example

Given the bar chart:

Red has the highest frequency and so it is the modal category.

Guidelines to analysing categorical distributions

• Start by mentioning context: what does the data represent and how many data points are there in total?
• Always mention the modal category, and its frequency
• If there is only a small number of categories (or you are told to do so), mention and compare all categories
• If there are a large number of categories, you don’t need to mention all of them, choose the most significant. Depending on the situation, this may be categories with very low or very high frequencies, categories with similar frequencies, or simply categories which are most relevant to the situation being analysed.
• When mentioning a category, always cite its frequency (preferably as a percentage).
• When analysing two-way frequency tables, try to find associations between the categories of the two datasets.

Example (1 dataset)

Assuming we recorded the colour of a number of marbles, given the frequency table:

An appropriate analysis would be: “The colour of 4 marbles was recorded. The modal colour was red, at 75%. The remaining 25% were blue”

Example (2 datasets)

Assuming we recorded the colour and size of a number of marbles, given the two-way frequency table:

An appropriate analysis would be: “The colour and size of 4 marbles was recorded. The mode was big and red with 50%. Of the remaining; 25% were small and red, and 25% were small and blue. The table shows that blue marbles were all small (100%), while red marbles were more likely to be big (66.67%) than small”.