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# Statistics GCSE AQA standard deviation watch

1. In all of my revision, I have been learning the two different formulas for standard deviation, one for a sample, and one for population. However, in the formula sheet for last years paper, they give 4 different formulas. One of them is the one I learnt for standard deviation of a population, but none of the others I recognise. Can someone please explain.

http://imgur.com/a/E8Cvy
2. All of those four versions are for a population.

The one that you recognise is the definition of the standard deviation for a population. However, it is very awkward to use in reality. Think of the amount of work involved. You would have to;

- work out the mean
- subtract the mean from each of your values (this is the bit that would take longest)
- square the result
- divide by n
- take the square root

The version next to it (the "or" version) is exacly the same thing after a bit of algebra (it involves expanding the squared bracket and a few other steps - it is not too hard, but you don't have to worry about this). It is much easier to calculate. Now, all you have to do is;

- work out the mean
- square all of the values, and add these up
- divide the sum of the squares by n, and subtract the square of the mean
- take the square root

If you try it with an example, you should see that this is much quicker.

It is important to understand the definition - that is the form that explains what the point of the standard deviation is - but in practice, the second version is much easier.

The other two forms are the same thing (definition and useful version), but are for when you have your data in a frequency table, rather than just a list of numbers. Have you done any questions like this?

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Updated: April 6, 2017
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