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 when comparing datasets using the mean and range interpreting the statistics is just as important as calculating them.
Students are taught to describe both the mean and range of datasets. However, the importance of what we can learn about the data from the range is poorly grasped. Often, the range is quoted without any context-based interpretation. This means students are losing out on marks in exams and are insufficiently prepared for the context-based answers as they progress in the statistics discipline.
I start the lesson with a reminder of the mean and range of datasets. I show how the range can be used to calculate the unknown value in a small data set. My aim is to plant the idea that the range is an effective tool used to gain a better understanding of a data set.
At this point in the lesson, students are confident using the mean and range to work out missing data.
We turn our attention to comparing two datasets. Students are asked to calculate the mean and range for each data set from the raw data presented.
At this point, I ask the class to compare the two datasets on their whiteboard. Most students describe one set of data as having a smaller or larger mean than the other. Very few students make any comment regarding the range.
I provide a written framework to help the students write a comparison. This encourages the class to think about the differences in the mean and range in the context of the data.
As we move on to the third slide students are ready to practise comparing datasets through a variety of scaffolded questions.
I encourage students to adapt the framework for each example by drawing appropriate conclusions about the within the context of the data. I hope 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. In future lessons students progress onto representing and interpreting datasets using stem and leaf diagrams.
My name is Jonathan Robinson and I passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.
Understanding the concept of the mean using multi-link cubes is key to finding the mean from a data in a frequency table.
Visual and algebraic methods for writing a single column vector.
How to teach working out the reciprocal of integers, fractions, decimals and mixed numbers.
How to teach proving geometrical properties using algebra.