In statistics, a 'variable' refers to a source (of data) that is measurable or observable. A variable could be something like temperature, mass, height, make of car, type of animal or goals scored. In most cases, we would expect a variable to change between each observation.
Data variables can be defined as either numerical or categorical.
Discrete numerical data involve data points that are distinct and separate from each other. There is a definite 'gap' separating one data point from the next. Discrete data usually, but not always, consists of whole numbers, and is often collected by some form of counting.
Examples of discrete data:
Number of goals scored per match | $1$1, $3$3, $0$0, $1$1, $2$2, $0$0, $2$2, $4$4, $2$2, $0$0, $1$1, $1$1, $2$2, ... |
Number of children per family | $2$2, $3$3, $1$1, $0$0, $1$1, $4$4, $2$2, $2$2, $0$0, $1$1, $1$1, $5$5, $3$3, ... |
Number of products sold each day | $437$437, $410$410, $386$386, $411$411, $401$401, $397$397, $422$422, ... |
In each of these cases, there are no in-between values. We cannot have $2.5$2.5 goals or $1.2$1.2 people, for example.
This doesn't mean that discrete data always consists of whole numbers. Shoe sizes, an example of discrete data, are often separated by half-sizes. For example, $8$8, $8.5$8.5, $9$9, $9.5$9.5. Even still, there is a definite gap between the sizes. A shoe won't ever come in size $8.145$8.145.
Continuous numerical data involves data points that can occur anywhere along a continuum. Any value is possible within a range of values. Continuous data usually consists of decimal numbers, and is often collected using some form of measurement.
Examples of continuous data:
Height of trees in a forest (in metres) | $12.359$12.359, $14.022$14.022, $14.951$14.951, $18.276$18.276, $11.032$11.032, ... |
Times taken to run a $10$10 km race (minutes) | $55.34$55.34, $58.03$58.03, $57.25$57.25, $61.49$61.49, $66.11$66.11, $59.87$59.87, ... |
Daily temperature (degrees C) | $24.4$24.4, $23.0$23.0, $22.5$22.5, $21.6$21.6, $20.7$20.7, $20.2$20.2, $19.7$19.7... |
In practice, continuous data will always be subject to the accuracy of the measuring device being used.
The word 'ordinal' basically means 'ordered'. Ordinal categorical data involves data points, consisting of words or labels, that can be ordered or ranked in some way.
Examples of ordinal data:
Product rating on a survey | good, satisfactory, good, excellent, excellent, good, good, ... |
Exam grades | A, C, A, B, B, C, A, B, A, A, C, B, A, B, B, B, C, A, C, ... |
Size of fish in a lake | medium, small, small, medium, small, large, medium, large, ... |
The word 'nominal' basically means 'name'. Nominal categorical data consists of words or labels, that name individual data points.
Examples of nominal data:
Nationalities in a sporting team | German, Austrian, Italian, Spanish, Dutch, Italian, ... |
Make of car driving through an intersection | Toyota, Holden, Mazda, Toyota, Ford, Toyota, Mazda, ... |
Hair colour of students in a class | blonde, red, brown, blonde, black, brown, black, red, ... |
Nominal data is often described as 'un-ordered' because it can't be ordered in a way that is statistically meaningful.
Which two of the following are examples of numerical data?
favourite flavours
maximum temperature
daily temperature
types of horses
Which one of the following data types is discrete?
The number of classrooms in your school
Daily humidity
The ages of a group of people
The time taken to run $200$200 metres
Classify this data into its correct category:
Weights of dogs
Categorical Nominal
Categorical Ordinal
Numerical Discrete
Numerical Continuous