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standard deviation

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:

∑i=1n∣(xi−xˉ)∣n\frac{\displaystyle\sum_{i=1}^n |({x}_i-\bar{x})|}{n}


(sorry if i messed that up, it was my first time. :colondollar:)
(edited 11 years ago)
Reply 1
Avatar for the bear
the bear
20
i think your formula

∑x=1N∣(xˉ−x)∣n\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
(edited 11 years ago)
Reply 2
Avatar for Zenomorph
Zenomorph
3
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)
Reply 3
Avatar for davros
davros
16
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:

∑i=1n∣(xi−xˉ)∣n\frac{\displaystyle\sum_{i=1}^n |({x}_i-\bar{x})|}{n}


(sorry if i messed that up, it was my first time. :colondollar:)


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.
oh.. i see. i wish they'd use that formula in s1, it's far more intuitive.

thanks for all of the replies guys. : )
(edited 11 years ago)
Reply 5
Avatar for davros
davros
16
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 :smile:

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