Skew in Histograms

Students examine real-life data, identify skew, and investigate the relationship between mean, median and mode for distributions with varying skew.

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Overview of task

Students examine real-life data, identify skew, and investigate the relationship between mean, median and mode for distributions with varying skew.

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Mathematical strand

Statistics

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Prior knowledge

This task should be accessible to most Core Maths students. The idea of skew can be introduced before this task (see below).

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Relevance to Core Maths qualifications

•AQA

•C&G

•Eduqas

•Pearson / Edexcel

•OCR

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Suggested approaches

If students have not already been introduced to the idea of skew, do this quickly by sketching three histograms on the board to show the three types of skew. Then allow students to work through the worksheet. They could work in pairs to estimate the positions for the mean, median and mode of each of the three distributions shown on the worksheet. The task provides a good opportunity to discuss results and the reasoning that led to them. Note that some students may not initially recognise Histogram 2 as being symmetric – especially if they are used to seeing ‘near perfect’ examples of symmetric distributions.

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Resources/documentation

If students have not already been introduced to the idea of skew, do this quickly by sketching three histograms on the board to show the three types of skew. Then allow students to work through the worksheet. They could work in pairs to estimate the positions for the mean, median and mode of each of the three distributions shown on the worksheet. The task provides a good opportunity to discuss results and the reasoning that led to them. Note that some students may not initially recognise Histogram 2 as being symmetric – especially if they are used to seeing ‘near perfect’ examples of symmetric distributions.

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Resources/documentation

The activity is presented as a single worksheet, ‘Identifying skew in histograms’.

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Relevant digital technologies

Students could use spreadsheets or other data-handling packages to draw histograms for other data sets – this would be particularly useful if tackling the investigative extension described below.

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Possible extensions

Although the task as presented is quite short, there is ample opportunity to extend it. For example, students could make up other sets of data in order to investigate the relationship between the skew of a distribution and the relative values of the mean, median and mode.