7.02 Classify data

Types of data

 

When we collect information for statistical purposes we refer to that information as data.  Data can be classified as numerical data or categorical data.

 

Numerical data

Numerical data can be counted, ordered and measured. It can be either continuous or discrete. Numerical data is also called quantitative data.

 

Continuous numerical data

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

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

Data for all of these examples could be anywhere on a scale interval and could even be fractions. For example, it might be $25.3$25.3 degrees or a man might be $182.13$182.13cm tall.

Notice that each of these examples is measured with some sort of instrument: a ruler, a set of scales, a thermometer, a stopwatch. Continuous data is almost always measured.

 

Discrete numerical data

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.

Examples of discrete data are the number of pets people have and the number of goals scored in a game and money.

Data for these examples will always have distinct values. We couldn't own $\frac{1}{4}$14​ of a dog score or score $2.5$2.5 goals in a game of soccer so there is no continuity between the scores.

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

Other examples of discrete numerical data include marks on a test, views on a video, votes for a candidate in an election, and how much money you have. Notice that each of these examples of discrete data is counted, not measured. Discrete numerical data is always countable.

 

Categorical data

Categorical data is non-numeric and is represented by words. It describes the qualities or characteristics of a data set. Categorical data is also known as qualitative data.

Examples include blood groups (A, B, AB or O) or hotel star ratings.

Categories may have numeric labels, such as the numbers worn by players in a sporting team, but these labels have no numerical significance; they merely serve as labels.

Categorical data can be either ordinal or nominal.

 

Ordinal categorical data

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 are another example of ordinal data. 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. So the finishing places can be ordered but the differences between the finishing times may not be the same between all competitors.

 

Nominal categorical data

For nominal data, the 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, you are giving categorical data numerical labels. You can count but not order or measure nominal data.

 

Practice questions

Question 1

Question 2