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    • Thread Starter
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    hello again!

    i've been finding it difficult to remember the (edexcel, s1) formula for variance (and hence standard dev). i mean if the standard deviation is used to measure the mean distance from the mean, then why isn't it calculated by:

    \frac{\displaystyle\sum_{i=1}^n |({x}_i-\bar{x})|}{n}


    (sorry if i messed that up, it was my first time. )
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    i think your formula

    \sum_{x=1}^N \frac{|(\bar{x}-x)|}{n}

    is for the Mean deviation not the Standard deviation


    PS it is

    latex]\sum_{x=1}^N \frac{|(\bar{x}-x)|}{n}[/latex
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    variance = sum of the SQUARED differences from the mean

    SD = Sq root of above

    Why the funky procedure ?

    Cause you have to eliminate any -ve summed values when calculating variance, afterwards you need to square root it to bring the values back down to size (otherwise they'd be too large and disproportionate to the sample values)
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    (Original post by genuinelydense)
    hello again!

    i've been finding it difficult to remember the (edexcel, s1) formula for variance (and hence standard dev). i mean, if the standard deviation is used to measure the mean distance from the mean, why isn't it calculated by:

    \frac{\displaystyle\sum_{i=1}^n |({x}_i-\bar{x})|}{n}


    (sorry if i messed that up, it was my first time. )
    As the bear points out, the formula you've given is called the Mean Absolute Deviation. It's another method of spread that is perfectly acceptable, but it's just defined differently from the standard deviation formula which involves squares and square roots.
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    oh.. i see. i wish they'd use that formula in s1, it's far more intuitive.

    thanks for all of the replies guys. : )
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    (Original post by genuinelydense)
    oh.. i see. i wish they'd use that formula in s1, it's far more intuitive.

    thanks for all of the replies guys. : )
    It's not just an S1 invention to be fair - you'll find Standard Deviation used all over the place in statistics, so it's worth getting used to the definition
 
 
 
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