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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.

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## Gwen Tresidder says:

I like the way you start, with the multilink towers. My bugbear is with the data you use later. I think students should be using real and meaningful data, not just any numbers that can be dreamed up so they divide conveniently with a spurious context that is uninteresting to students. You are right that they always find this procedure, mean from frequency table, difficult. But I would suggest that if the data were such that the mean meant something that they cared about, then they would be more likely to notice when they get a ridiculous answer (which is almost always the effect of carrying out the procedure incorrectly). Furthermore, they are more likely to really understand what the mean is, why we use it, and its power. It's not easy finding good raw data, but I'd argue it is essential. At least if you collect shoe sizes from the class you are using real data, and students will have to deal with all the grey areas of numbers that don't necessarily divide nicely, but who is really interested in who has bigger feet? I've done a stats project a couple of times with Y8s where they collect data on amount of housework each child does at home - interesting comparisons between girls and boys, eldest siblings and others etc. etc. And believe me, they really do care!! And they have to deal with all the questions of respondent honesty, varied interpretation etc. etc. I think if we are to develop a genuine understanding in what statistics is, we have to make it meaningful, not a set of procedures to be memorised.

## mrmath_admin says:

Hi Gwen

Many thanks for the comment. I agree the data has to be meaningful and of interest to the students. Too often students have to answer questions on things they have little or no interest in which makes the mathematics seem boring.

I used shoe size as the first example on this new topic because in my experience boys and girls can relate to it and like you mentioned it does lead on to collecting a set of primary data once the students have worked through their first question.

I like to scaffold the learning in lessons so students can focus on the intended learning objective at the start. When they become more confident with applying this skill we, as you suggest, introduce other aspects that are relevant to the subject matter.

Many thanks for taking the time to respond to my blog.