Why Do We Calculate Standard Deviation the Way We Do?
Date: 02/05/2004 at 00:52:43 From: Greg Subject: Standard Deviations Why do we square the deviations and then take the square root when calculating standard deviation? Why can't we just take the absolute value of the deviations? I've tried similar calculations, and the answers are close, but in most cases, squaring appears to be more correct.
Date: 02/05/2004 at 11:16:40 From: Doctor George Subject: Re: Standard Deviations Hi Greg, Thanks for writing to Doctor Math. There is more than one way to measure the spread of a distribution. Having different methods is a separate issue from the issue of accuracy. Taking the sum of absolute deviations is a perfectly valid method, but it will in general lead to a different result from standard deviation. The two methods characterize the spread of the distribution in different ways. I can think of two reasons why the absolute method is not commonly used. 1. When independent random variables are added their variances add. Remember that variance is the square of the standard deviation. 2. Variance has the property of being differentiable, which becomes helpful in estimation theory. Absolute deviations do not have these two important properties. Does that make sense? Write again if you need more help. - Doctor George, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.