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Average and Standard Deviation

October 21, 2018

What does average mean?

When putting together some slides for this section of Core Maths, I put in the question “What does average mean?” I realised I didn’t actually know where the word comes from so I used Google’s etymology search and found that it comes from a time when cargo ships would be transporting goods around. Sometimes the goods would be damaged and the French word avarie is “damage to ships or goods”. The decision as to how to fairly share out the costs was developed and the suffix -age from the word damage was used. Eventually, this word came to be associated with a more general sense of sharing things out as is done in the mean.

How does Standard Deviation work?

I’ve also been  teaching the Standard Deviation. I made a point of going through the long calculation (even though it’s not needed for this course) as I think it’s important to try and understand what is going on rather than blindly use a calculator. It’s not a complex process and most students were fine with following it along. I also think it gave them an even better appreciation for the power of practising with their calculator modes (given the alternative process!)

When does Standard Deviation matter?

To help come up with situations where standard deviation is important I asked Twitter to suggest scenarios and got a nice list. I’m working on putting these into a worksheet (which I’ll share once it’s ready) but I wanted to thank all those that contributed. I discussed this and the etymology of average on episode 61 of my podcast Wrong, but Useful.

Mean and Standard Deviation in Psychology

In terms of comparing data sets using mean and sd, I went looking for other questions and found this one on an AQA A level Psychology paper. (Note that there’s no expectation for them to be able to calculate the sd in that course.)

Psychology Q Mean and SD table

Psychology Q Mean and SD question

I think it’s worth noting that it’s 4 marks and looking at the mark scheme is interesting too:

Psychology Q Mean and SD answer

The Examiner’s report on this question is eye-opening too:

Although there were some strong responses, generally students found this harder than anticipated.A number failed to receive any credit due to simply defining the mean and the standard deviation. It was also far too common for students not to understand and answer the ‘justify’ component of the question. Many students simply restated information from the table or provided possible explanations or conclusions, as opposed to justifications. Although students generally saw the mean as showing a difference, there was often the claim that music hindered performance, with confusion regarding time being a higher score, meaning slower. Worryingly, some students still have little understanding of standard deviation.

Hopefully that’s given you some things to think about regarding this topic and our course will help with that bolded section above!

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