ParkStein wrote in message <[EMAIL PROTECTED]>... >Hi everybody, > >with my hope that I can get the answer here, >I send you my question. >When I'll get the SD in a data, >why do I use the square of the difference >between average and the respective value >instead of the absolute value of the difference? > >why root (sigma (average - x(i))^2) ? >why not sigma |average - x(i)| ? > >thanks >
It's a matter of choice. For the normal distribution, you can obtain an unbiassed estimate of the variance from the squared deviations from the mean. Taking the square root though gives a biased estimate of the std. deviation. The argument for using absolute deviations is that it is less influenced by extreme observations. If the influence of outliers is an important consideration, then absolute deviations from the MEDIAN are usually preferred to deviations from the mean. Cheers -- Alan Miller (Honorary Research Fellow, CSIRO Mathematical & Information Sciences) http://www.ozemail.com.au/~milleraj http://users.bigpond.net.au/amiller/ . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
