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Why square to get the standard deviation?
Message posted by Martin V憴ina (via 24.202.84.181) on July 2, 2001 at 10:15 PM (ET)
Hi,
I'm wondering why we square each of the distances to the mean when we calculate the standard deviation. I know that the numbers added have to be positive, but then why not just add the absolute values?
If we add the absolute distances to the mean and divide the result by the number of values, it doesnt give the same value as when we square the distances, divide by number of values and then square root, right? So the standard deviation is not a mean of the distances to the mean? Why is that?
Thanks
Martin
READERS RESPOND:
(In chronological order. Most recent at the bottom.)
Re: Why square to get the standard deviation?
Message posted by JG (via 128.8.22.32) on July 3, 2001 at 3:09 AM (ET)
The two parameters of the Normal or Gaussian distribution are mean and variance. Consequently, the standard deveation - square root of variance - has become a standard measure of variability with much easier to workwith mathematical properties than the average absolute deviation. We then get sampling distributions using the mean and standard deviation from the Central Limit theorem - something that is much harder to get for the mean absolute deviation.
standard deviation
Message posted by ron stark (via 209.131.198.181) on September 26, 2001 at 9:33 PM (ET)
how do you find standard deviation?
Re: Why square to get the standard deviation?
Message posted by Phil (via 216.175.115.238) on September 29, 2001 at 3:18 PM (ET)
Martin - You have a reasonable question and the first response essentially answered it. The squared-distance formula (variance) has much better mathematical properties than the average absolute distance formula. It is much easier to work with also. For example, using the variance (or standard deviation) to make inferences from sample data, you will make fewer Type II errors than if you used the average absolute difference.
If you took a sequence of courses in "Mathematical Statisitics" you would get enough theory on this to choke a horse.
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