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    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.


    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
    - add them all up
    - 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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