In this blog I will discuss finding the mean average from a frequency table. Students need to understand why the average is the total of the data divided by the sample size. I like to use multi-link cubes to demonstrate this concept.
The first step when finding the mean average of data in a frequency table is to calculate the sum of the data. This begins with a discussion of what the total shoe size would be if all the students placed their feet in a line? By working through the problem this way it becomes intuitive to find the product of the shoe size and frequency.
I demonstrate how to calculate the boy’s shoe size and ask the class to find the girl’s. I find this example works well as most students would expect boys to have a larger shoe size so this backs that up.
If the class is large enough I put a student in charge of collecting shoe sizes for boys and girls and repeat the question using primary data. It’s always funny when boys are proud to have largest feet in the class.
Moving on from this I ask the class to work through the question on the third slide using mini-whiteboards. I use mini-whiteboards for this as there is quite a bit of working out involved and it helps the students keep track of their method. It also helps me to assess the progress so I can feedback.
The plenary takes between 10 to 15 minutes. I think it’s important to leave plenty of time for this as some students can be a little overwhelmed with making sense of the question because data is normally presented to them in a table. In this question however they have to read the frequencies of a bar chart. To save time I would print a copy of the bar chart as a handout. Students sitting at the back of the classroom can struggle to read the correct frequencies of the bar chat.
I find students need at least a couple of lessons interpreting data from frequency table so the following lesson is normally about finding a combination of the median, mode, mean and range from frequency tables.
Do you have any nice examples for teaching the mean average or how to work with frequency tables? Please leave a comment to share your ideas.
Schemes of Work for Maths Teachers As a Head of Maths I understand the importance of a detailed, flexible and simple scheme of work. I designed the Key Stage 3 and GCSE schemes of work for maths teachers available at mr-mathematics.com to be just that. They are fully aligned with the current specifications and are […]
Solving Problems with Non-Right-Angled Triangles Solving problems with non-right-angled triangles involves multiple areas of mathematics ranging from complex formulae to angles in a triangle and on a straight line. As the GCSE mathematics curriculum increasingly challenges students to solve multiple step problems it is important for students to understand how to prove, apply and link […]
When factorising algebraic expressions with powers students often struggle to identify the highest common factor when it involves an algebraic term. For example, factorising 3h + 12 as 3(h + 4) is attempted correctly much more often than factorising 3h2 + 12h as 3h(h + 4). In this lesson students learn how to identify the […]