Home > #MTBoS, Maths, Teaching > What does it mean?

What does it mean?

Today my year 11s were busy revising ahead of tomorrow’s mock exam and one of them started singing the averages song. You know the one:

“Mean is average, mean is average, mode is most, mode is most, median’s the middle, median’s the middle, range high low, range high low.”

This got me thinking about the words we use. I’ve always disliked this song as a mnemonic as it encourages people to think of the mean as the “average” when actually the mode and the median are also averages too. The median in particular is a very useful one and we need pupils to understand the distinction. I have been very impressed in recent staff meetings to hear the principal, an English teacher by trade, use the term “national median” rather than “national average”!

As I was thinking about this, though, I had the sudden realisation that I should also be feeling the same way about the term “mean”! Granted, at GCSE level we only talk about one mean, the arithmetic mean, but that doesn’t mean the geometric mean doesn’t exist. (Nor the root mean square nor harmonic mean for that matter! Other means are available)

This is a hypocrisy in the way we treat certain words. I’m not the only maths teacher who dislikes the way mean and average have become synonymous. But no one has ever mentioned that the word arithmetic is missing from the term every time we use it.

I worry that we may be setting students who go on to further study statistics up for confusion in the future by simply referring to the arithmetic mean as the mean.

Have you ever used the term arithmetic mean, or even geometric mean, with your students? Have you shared my worry? Or do you think I’m being overly pedantic and it doesn’t matter? I’d love to hear your opinion.

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  1. April 29, 2014 at 8:58 pm

    I’ve noticed even maths exams use “average” sloppily. Look at questions about bills: they’ll frequently say “Ben uses an average of 6 litres a day” or whatever, and want you to work out the total usage for the year. Technically you can only do that if you know it’s the arithmetic mean.

    • April 29, 2014 at 9:01 pm

      I’ve not noticed that, but I’m certain I will now! It is terrible that the boards are at it. Which do you use? I’ll be checking my edexcel papers in the morning!

  2. April 30, 2014 at 3:01 pm

    Reblogged this on The Echo Chamber.

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