Describing Variables (College Board AP® Statistics)

Categorical & quantitative variables

What is categorical data?

• Categorical data is data that is usually given in words and not numbers to describe something

  • It is also known as qualitative data

  • e.g. the colour of a teacher's car, a student's grade level, movie genres etc.

What is quantitative data?

• Quantitative data is data that is given using numbers which count or measure something

  • e.g. the number of pets that a student has, the mass of a kitten, the time taken to run 100 m etc.

Discrete & continuous variables

What is discrete data?

• Discrete data is quantitative data that uses a countable number of values

  • Discrete data takes specific values from a set of values

  • e.g. shoe size, 6, 6.5, 7, 7.5, 8, ... etc.

  • The number of values may be finite (e.g. integers from 1 to 5) or may be countably infinite (e.g. positive integers)

What is continuous data?

• Continuous data is quantitative data that needs to be measured

  • Continuous data can take any value within a range of infinite values

    • e.g. the height of a student

  • Given any two values, it is always possible to find another value in between

    • e.g. 4.58 and 4.59 has 4.585 in between

When are variables discrete or continuous?

• Some variables can be considered as discrete or continuous depending on the context and how it is defined

  • For example, age can be discrete or continuous

    • If you mean how many years old a person is then this is discrete

    • If you mean how long a person has been alive then this is continuous

• When data is collected it is always collected in a discrete manner

  • However, when considering a model of the data, it is important to remember that it may be continuous

  • E.g. data may be collected on the length of leaf from a particular type of tree

    • The data collected may be measured to the nearest cm

    • but the data itself is continuous