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February 20th, 2013, 01:10 PM   #1
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Standard deviation and Variance

I was working on a statistical problem involving variance and standard deviation recently, and I've never really understood why we need to find the variance in order to get standard deviation. So i did a couple of examples using the absolute values of the difference between the mean and any point x, and i also used the variance method i.e taking the square root of the difference between the mean and any point x. I noticed that the variance method always gives you a higher standard deviation. Basically my question is this, is variance used to find standard deviation because it gives you a higher number and so reduces the probability of over estimation? or is there another reason?
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February 20th, 2013, 01:21 PM   #2
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Re: Standard deviation and Variance

One main reason the variance is used is that it is easier to calculate, particularly in the case where further data is added in. When using absolute difference, everything has to be calculated from scratch, while using the variance requires simply updating the first and second moments.
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February 20th, 2013, 01:33 PM   #3
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Re: Standard deviation and Variance

Thanks, mathman. That makes sense.
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