In my experience, students, in general, find the concept of a mean straightforward to calculate and understand. However, the mean alone does not provide a complete picture of a set of data. To achieve this, a measure of spread is also required. The range is the simplest measure that can be used for this. Not only can a range be used to describe a dataset, in simple examples, and in combination with other information, it can also be used to calculate missing pieces of data. In this blog I discuss that when comparing datasets using the mean and range interpretating the statistics is just as important as calculating them.
Students are taught to describe both the mean and range of a dataset but often, the importance of what we can learn about the data from the range is poorly grasped and the range is quoted without any context-based interpretation. This means that not only are students losing out on marks in exams, but they are not gaining the preparation for the more narrative context-based answers that can be required as they progress through their education in the statistics discipline.
I start the lesson with a reminder of the mean and range of a dataset. However, rather than presenting the range as just a value to be calculated, I showed how it can be used to calculate the unknown value in a small dataset. I aim to plant the idea that the range isn’t just an insignificant value, but rather a tool that can be used to gain a better understanding of a dataset.
At this point in the lesson, students have a conceptual understanding of the mean and range and have gained confidence in using the clues provided by them to solve for missing information in the data.
We then turn our attention to using the mean and range in a comparison of two datasets. Students are first asked to calculate the mean and range for each dataset from the raw data presented. These will be familiar and straightforward calculations for them and should be relatively quick to perform. It is at this point that when asked to draw comparisons between two datasets, most students will describe one mean as being larger or smaller but often with no reference to the dataset in question and almost always with no comments on the ranges.
I provide a written framework to describe the comparison of datasets that students complete with the appropriate figures and descriptions. It encourages students to think about the differences in the means with reference to the example and to also ensure that reference to the range is always included alongside any comparison of means.
Students now practise comparing datasets using the mean and range through a variety of scaffolded questions. The emphasis being on adapting the written framework for each example and drawing appropriate conclusions about the data, rather than performing the calculations for the summary statistics. I believe this framework can make the narrative context-based style of interpretation both second nature and less intimidating to students.
Comparing datasets using the mean and range is the third lesson in the comparing and summarising data scheme of work. To consolidate their learning there are some excellent resources available in the Measures of spread section at nrich.maths.org. Resourceaholic shares some nice resources on measures of spread and location too. In future lessons students progress onto representing and interpreting datasets using stem and leaf diagrams.
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