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**Differentiated Learning Objectives**

By the end of the lesson:

- All students should find the median from a box and whisker diagram.
- Most students should find the median and interquartile range from a box and whisker diagram to comment on a distribution.
- Some students should compare the average and spread of multiple distributions from box and whisker diagrams.

Ask students to work in pairs to make a comparison of boys and girls IQ from the dot plot shown.

**Prompts / Questions to consider**

- Does the dot plot show which gender has the higher IQ?
- What does the dot plot show about the spread of the IQ for boys and girls?
- Which part of the dot plot draws your attention the most? Why?

Progressing on from the dot plot, discuss how box and whisker diagrams are like dot plots in that multiple data sets can be aligned on the same number line for comparison. One of the key differences between them being box plots focuses attention on the middle 50% of data; this is called the interquartile range. Box plots also indicate the median average, which is hard to tell from a dot plot.

After demonstrating the key features of a box and whisker diagram and how to use them to compare datasets, pose the question below for students to work through in pairs.

**Prompts / Questions to consider**

- What does the median tell you about how students performed on each test?
- What does the interquartile range tell you about the spread of results on each test?

In the plenary, I ask students to compare the distribution of heights for students in years 7 to 11. Encourage students to share their comparisons with their peers to refine and justify their reasoning.

**Prompts / Questions to consider**

- What is happening to the median over time? Why?
- What is likely to be the cause for the change in interquartile range over time?
- How might these box plots change if we drew separate sets for each gender?

Engage and inspire your students while reducing your lesson planning with a Mr Mathematics membership.

August 5, 2022

Year 13 Further Mathematics: Statistics 1: Geometric and Negative Binomial Distributions

July 26, 2022

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