1.01 Types of data

Numerical data is data that can be counted, ordered and measured. It is sometimes also called quantitative data.

Numerical data can be either continuous or discrete.

A data set is continuous if the values can take on any value within a finite or infinite interval interval.

Examples of continuous data are height, weight, temperature or the time taken to run 100 metres.

Notice how all of these examples could be anywhere on a scale interval, including fractional and decimal values. For example, it might be 25.3\degree C, or a man might be 182.13 cm tall.

A data set is discrete if the numerical values can be counted but are distinct and separate from each other. They are often (but not always) whole number values.

Some examples of discrete data are: the number of goals scored in a game, the number of people in a class, the number of pets people have.

Notice how all these examples have distinct values. For example, you couldn't score 2.5 goals in a game of soccer or own \dfrac{1}{4} of a dog, so there is no continuity between the scores.

In some tournaments, half a point is awarded for a draw. In this case, there could be a score of 2.5, but there still could not be scores of 2.25 or 2.75 and so on, so the data is still discrete.

Examples

Categorical data is non-numerical. In other words, it describes the qualities or characteristics of a data set. Categorical data is sometimes also called qualitative data.

There are two types of categorical data: ordinal and nominal.

A set of data is ordinal if the values can be counted and ordered but not measured.

Rating scales are examples of ordinal data. The finishing places in a race is another example of ordinal data.

Think about it - the positions in a race can be ordered or ranked. Finishing first means you were faster than the person who came second and the person who finished eighth was slower than the person who finished sixth.

However, the differences between the finishing times may not be the same between all competitors. Check out the picture above. The times between first and second will be really close - probably within half a second - however the time between second and third will be longer. There is not a fixed interval.

The word nominal basically means name. In other words, data is split up based on different names or characteristics. Nominal data may be the names of countries you have visited or your favourite colours. We could assign these different characteristics a number where the numbers are labels. In other words, we are giving categorical data numerical labels. We can count but not order or measure nominal data.