Standard deviation =! average distance from mean
Hi folks, I'm new to WikiEducator, came across this page by happenstance. I noticed that in a couple of places, the article defined the standard deviation as "the average distance from the mean". This is a common belief and intuitively "sounds true" but unfortunately it's simply not the case. The standard deviation is close to the average distance from the mean (i.e. the mean absolute deviation), but will in almost all cases be larger than the mean absolute deviation. This can be easily verified (try it). Taking the Falcon example in the article, for instance, the standard deviation is 4, but the mean (absolute) deviation is 3. Incidentally, the difference isn't just due to the use N-1 in the variance/SD formula. This article discusses the difference between the SD and mean deviation: http://www.tandfonline.com/doi/abs/10.1111/j.1467-8527.2005.00304.x I've made some rudimentary changes to the article to address this misconception. Mattnz 05:57, 5 April 2012 (UTC)
Thank you for your comments and revisions. I agree that the wording incorrectly equated the sd with average distance from the mean. When I worked on the page awhile back, I was contemplating creating some pages for use by students interested to learn statistics, but who find the mathematical side of stats challenging. The standard deviation is a concept that these students struggle to understand conceptually. I think these students would find the absolute mean deviation easier to understand. I wish I had access to the full article you provided...it would certainly be going against the tide to have them focus on the mean difference rather than the sd, but maybe it could be used as a way in to understanding the sd. Something to think about.
I got the idea to use "average distance from the mean" as a way to understand the idea of sd, conceptually, from the page presenting the concept of standard deviation, at the Open Learning Initiative. But I see now that the use of the word "average" in this context is clearly defined as "typical", and I didn't make this connection on this page.
Thanks for your feedback. Alison