History of standard deviation

Home > Statistics Every Writer Should Know > The Stats Board > Discusssion

History of standard deviation
Message posted by Sophia on November 23, 1999 at 12:00 AM (ET)

Can someone tell me some information about history of standard deviation ? Who invited this idea / formula ?

And why the formula divide n not Sq(n)

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: History of standard deviation
Message posted by Jack Tomsky on November 23, 1999 at 12:00 AM (ET)

Suppose you have a sample of size n from a normal distribution with an unknown mean. Any estimator of the variance involves dividing the sum of squares about the sample mean by a divisor.

Just to get you all confused, the following theoretical properties are held by estimators with different divisors.

To get an unbiased estimate of the variance, divide by n-1.
To get the maximum likelihood estimate, divide by n.
To get the minimum mean-squared-error estimate, divide by n+1.

The estimate of the standard deviation is obtained by taking the square-root of the variance estimate. For large sample sizes, these nuances don't matter too much in practice.

Re: History of standard deviation
Message posted by JG on November 24, 1999 at 12:00 AM (ET)

The words 'average' and 'variability' are not very precise. If one assumes that the data has a 'normal' distribution, then the arithmetic mean is the natural definition of average and the standard deviation the natural measure of variability.
The formula for standard deviation is what it has to be in order to have the standard deviation in the same units as the mean and the original data. In fact, we should devide by (n-1) for sample data. A good introductory book on statistics should explain things further.

Your $5 contribution helps cover part the $500 annual cost of keeping this site online.