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**Differentiated Learning Objectives**

- All students should plot and interpret frequency diagrams for data presented in a frequency table.
- Most students should plot and analyse frequency diagrams and frequency polygons for data presented in a grouped frequency table.
- Some students should be able to compare distributions using frequency polygons.

**Links to Lesson Resources (Members Only)**

Students work out the mean, median and modal average from data presented in a frequency table. Students should have a good understanding of the modal average. Still, they may need guidance in calculating the median. The aim is to recap these static values to progress onto identifying trends later in the lesson.

**Prompts / Questions to consider**

- Do the mean average, median, and mode have to be equal?
- Is the mean or median likely to be greater than two goals per game?
- What is the range of goals scored per game?

Click here to view the video.

When drawing frequency diagrams, students need to understand the difference between continuous and discrete data. Discrete data can only take exact values. Continuous data can take any value and cannot be measured exactly.

A bar chart can be used to display grouped discrete data.

A histogram is used to display grouped continuous data.

**Prompts / Questions to consider**

- Is the data discrete or continuous?
- Should the bars touch each other or have a gap between them?
- Can/should the same scale be used for both days?

Students compare distributions using two frequency polygons. Emphasise that it is essential that they justify their response using different segments of the frequency polygon. Students could work in pairs to question and convince each other. Then, have students peer assess by some groups sharing their reasoning with the rest of the class. This activity takes between 5 and 8 minutes.

**Prompts / Questions to consider**

- What is the trend of each graph?
- Why do the polygons peak and then dip?
- In which subject did students perform the best/worst?

More able students could be given a frequency polygon and asked to work backwards to estimate the mean average. Less able students may need to have the axes scale provided for them.

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Scheme of Work: A-Level Applied Mathematics: Statistics 2: Conditional Probability