Mathematics level 9 - Statistics and probability

Teaching context - Numerical and categorical variables

At this level, students will investigate questions where the data contains both numerical and categorical variables.

Before conducting any investigations, students should be clear on the difference between numerical and categorical data. 

Numerical or quantitative data contains numbers that can either be counted (discrete) or measured (continuous). 

Categorical or qualitative data represents characteristics of the data. This data can be ordinal, meaning whilst the data is placed into groups or categories there is some order also involved. For example, smoothies sizes small (S), medium (M), and large (L). In this example the order of the smoothie size has significance. 

Categorical data can also be nominal, meaning the data cannot be ordered. For example, gender: female or male. In this example, the order of the data has no significance.

To ensure students have a good understanding of the different types of data provide multiple examples where they are required to label the data accordingly.  

A common misconception is that students may assume that any data containing numbers is numerical. Students need to understand that categorical data can include numbers. For example, postcode or a ranking from zero to four, etc. The numbers in these cases represent categories but they do not have any mathematical meaning. For example, the mean cannot be found for data involving postcodes.

Students will use their knowledge of numerical and categorical data to investigate everyday questions and issues that involve both types of data. For example, they may compare maximum temperatures for different towns in Victoria. In this example, the towns will be categorical data and the maximum temperatures will be numerical data. 

They can collect data from reliable secondary sources to create appropriate questions and conduct their investigation.

A secondary source is one where the data is collected by someone else. For example, the Australian Bureau of Statistics and the Bureau of Meteorology are secondary sources.

Teaching idea - Statistics in the media

In this activity, students will examine a newspaper or online resource to find examples of how data is used in the media, and how data can be relevant to everyday life:

  • Students work in small groups (two or three) to identify data from either a newspaper or other media source. They may use articles or advertisements or other resources to gain this information.
  • Once they have identified the data, ask them to organise it into numerical/categorical/both/unsure.
  • When organising into numerical and categorical, guide students to look at what is being measured, not how the results are presented. For example, 'nine out of ten people love this shampoo' is highlighting whether people love the shampoo or not, so the variable here is categorical, even though the data is presented using numbers.
  • Ask students to share their examples with the class and discuss emphasising the difference between categorical and numerical data.
  • Upon completion, allow students time to reorganise their items. Groups can then join together to check each other's work.

Extension ideas

  • Pre-test students on their graphing knowledge so high-ability students can have their curriculum compacted and extended. High-ability students could be grouped together for this task. Grouping these students together allows them to work at a similar pace and level of complexity. This creates a greater level of challenge for them as they collaborate on the task.
  • Ask students to provide a comparison of the features of numerical and categorical variables and how they are used within investigations. This will allow high-ability students to use their higher order thinking skills. Requiring high-ability students to make comparisons will ensure they are using their higher order thinking skills.
Original lesson plan available on the Maths Curriculum Companion