Re: Mean and Standard Deviation
Edward Dreyer wrote: > > A colleague of mine - not a subscriber to this helpful list - asked me if > it is possible for the standard deviation > to be larger than the mean. If so, under what conditions? Of course - for example, if you analyse mean-corrected data... It can even happen with data that are strictly positive. The log-normal distribution with sigma-squared>ln(2) is an example that has standard deviation larger than the mean; e.g. with sigma-squared=1, the standard deviation will be about 130% of the mean. Glen = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Mean and Standard Deviation
Of course the SD can be larger than the mean. If this were not so we would not have the standard normal... If the variable can take negative values, the mean may be close to zero, or even negative - while the SD has to be positive. If the variable can not take negative values, it is still possible for the SD to be larger than the mean, but the distribution will then be not symmetric. Alan Edward Dreyer wrote: > > A colleague of mine - not a subscriber to this helpful list - asked me if > it is possible for the standard deviation > to be larger than the mean. If so, under what conditions? > > At first blush I do not think so - but then I believe I have seen > some research results in which standard deviation was larger than the mean. > > Any help will be greatly appreciated.. > cheersECD > > ___ > > Edward C. Dreyer > Political Science > The University of Tulsa > > > = > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > = -- Alan McLean ([EMAIL PROTECTED]) Department of Econometrics and Business Statistics Monash University, Caulfield Campus, Melbourne Tel: +61 03 9903 2102Fax: +61 03 9903 2007 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Mean and Standard Deviation
Well, yes. the mean and standard deviation are not 'linked' for data with a Normal distribution. Dale Glaser asked: Well, what about the standard normal distribution: N(0,1)? The mean is 0, the standard deviation, 1. If you add the restriction that the data not be less than 0, and allow a severe skew (relax the Normal dist. requirement), then Ken Beath and others showed that yes, certainly, s can be larger than x-bar (or sigma > mu, if you prefer). Since the Poisson distribution _is_ linked, so that the mean equals the variance, then for an equivalent distribution (log-normal?), one sould expect that for mu values less than 1, the sigma (sqrt(var)) will be greater than the mean. Jay Edward Dreyer wrote: > A colleague of mine - not a subscriber to this helpful list - asked me if > it is possible for the standard deviation > to be larger than the mean. If so, under what conditions? > > At first blush I do not think so - but then I believe I have seen > some research results in which standard deviation was larger than the mean. > > Any help will be greatly appreciated.. > cheersECD > > ___ > > Edward C. Dreyer > Political Science > The University of Tulsa > > > = > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > = -- Jay Warner Principal Scientist Warner Consulting, Inc. North Green Bay Road Racine, WI 53404-1216 USA Ph: (262) 634-9100 FAX: (262) 681-1133 email: [EMAIL PROTECTED] web: http://www.a2q.com The A2Q Method (tm) -- What do you want to improve today? = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
RE: Mean and Standard Deviation
Title: RE: Mean and Standard Deviation Well, what about the standard normal distribution: N(0,1)? Dale N. Glaser, Ph.D. Pacific Science & Engineering Group 6310 Greenwich Drive; Suite 200 San Diego, CA 92122 Phone: (858) 535-1661 Fax: (858) 535-1665 http://www.pacific-science.com -Original Message- From: Simon, Steve, PhD [mailto:[EMAIL PROTECTED]] Sent: Friday, October 12, 2001 3:27 PM To: 'Edward Dreyer'; [EMAIL PROTECTED] Subject: RE: Mean and Standard Deviation Edward Dreyer writes: >A colleague of mine - not a subscriber to this helpful >list - asked me if it is possible for the standard deviation >to be larger than the mean. If so, under what conditions? > >At first blush I do not think so - but then I believe >I have seen some research results in which standard >deviation was larger than the mean. Well, if the mean is negative, then it is indeed very possible for the standard deviation to be larger. I suspect that you were considering the special case where the variable is non-negative. Then it is still possible for the standard deviation to be larger than the mean. In this special case, it serves as evidence of a highly right skewed distribution. Steve Simon, [EMAIL PROTECTED], Standard Disclaimer. http://www.childrens-mercy.org/stats
Re: Mean and Standard Deviation
In article <[EMAIL PROTECTED]>, Edward Dreyer <[EMAIL PROTECTED]> wrote: > A colleague of mine - not a subscriber to this helpful list - asked me if > it is possible for the standard deviation > to be larger than the mean. If so, under what conditions? > Easily. Any highly skewed distribution will produce this. For example enter 1,1,1,1,1 into a stats program and look at the descriptive statistics. Ken = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Mean and Standard Deviation
At 04:32 PM 10/12/01 -0500, you wrote: >A colleague of mine - not a subscriber to this helpful list - asked me if >it is possible for the standard deviation >to be larger than the mean. If so, under what conditions? what about z scores??? mean = 0 and sd = 1 >At first blush I do not think so - but then I believe I have seen >some research results in which standard deviation was larger than the mean. > >Any help will be greatly appreciated.. >cheersECD > >___ > >Edward C. Dreyer >Political Science >The University of Tulsa > > > > > > >= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >= > == dennis roberts, penn state university educational psychology, 8148632401 http://roberts.ed.psu.edu/users/droberts/drober~1.htm = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
RE: Mean and Standard Deviation
Title: RE: Mean and Standard Deviation Edward Dreyer writes: >A colleague of mine - not a subscriber to this helpful >list - asked me if it is possible for the standard deviation >to be larger than the mean. If so, under what conditions? > >At first blush I do not think so - but then I believe >I have seen some research results in which standard >deviation was larger than the mean. Well, if the mean is negative, then it is indeed very possible for the standard deviation to be larger. I suspect that you were considering the special case where the variable is non-negative. Then it is still possible for the standard deviation to be larger than the mean. In this special case, it serves as evidence of a highly right skewed distribution. Steve Simon, [EMAIL PROTECTED], Standard Disclaimer. http://www.childrens-mercy.org/stats
