Types of Statistical Variables

The characteristic of a variable is a common trait shared by the elements of a set.

A qualitative variable takes the form of a word, expression or code (colour, password, spoken language, etc.). It is not a quantitative trait.

A quantitative variable takes the form of a number or quantity. Depending on the nature of this number, this variable can be either discrete or continuous.

• A discrete quantitative variable can only have certain values within a given range. In general, these are quantities that can be counted, meaning they are natural numbers.

• A continuous quantitative variable can have any value in a given range. These are quantities that are real numbers.

The difference between discrete and continuous is not always easy to understand. For example, is a person's age a discrete or continuous variable? A person ages continuously, that is, at every moment. Age is therefore a continuous variable. However, when compiling data, it is possible to consider a person's age as a discrete quantitative variable. This is because, when people are asked their age, they answer with a natural number such as $12$ years, $25$ years or $87$ years and not $12.36$ years.

Just because the data collected is represented by numbers does not mean that the variable's characteristic is necessarily quantitative. For example, if we are looking at the area code of a telephone number, the answers could be $450,$ $418,$ $514,$ and so on. These number combinations do not represent a quantity, but instead represent codes. It is therefore a qualitative variable, not quantitative.