This task introduces students to the use of histograms to display sets of grouped data with unequal class intervals. The activity uses a PowerPoint presentation to explain why Frequency Density is a useful way of displaying data in these cases.

Overview of task

This task introduces students to the use of histograms to display sets of grouped data with unequal class intervals. The activity uses a PowerPoint presentation to explain why Frequency Density is a useful way of displaying data in these cases.

Strand

Statistics

Prior knowledge

This material will have been covered by some students at Higher Tier GCSE, and could usefully be used as a reminder where needed, as well as serving as an introduction to the topic for those who have not met it before.

Relevance to Core Maths qualifications

•AQA

•C&G

•Eduqas

•Pearson / Edexcel

•OCR

Suggested approaches

Work through the first slide to illustrate that there is a problem with using a standard bar chart for data with unequal class intervals. Explain that the eye and brain tend to compare areas rather than the heights of the bars; Frequency Density ensures that the areas of the bars are proportional to their areas. Then work through the next three slides, which provide further examples of drawing histograms, before showing the final slide, with examples of data sets for students to plot.

Resources/documentation

The PowerPoint presentation includes all of the examples and questions needed.

Relevant digital technologies

Students could use an appropriate graph-plotting program to produce the diagrams, although they will also benefit from the process of drawing at least some of them ‘by hand’.

Possible extensions

Students could extend this activity by finding their own sets of data to plot histograms for. It might also be useful to look at the effect of grouping a raw set of continuous data into intervals of various unequal sizes.

Acknowledgement

Developed by Nicola Letts of the Duston School, Northampton.