Range or Standard Deviation?
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 This topic has 4 replies, 5 voices, and was last updated 19 years, 4 months ago by Gabriel.

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March 27, 2003 at 1:16 pm #31805
Whilst running some basic SPC training, I was asked, “Why don’t you use 33% of the range to give you a value for standard deviation rather than do all the calculations?” This came after I pointed out that approximately 68% of data was within +/1 std devs of the mean.
Damn good question I thought!
How would others have replied?0March 27, 2003 at 4:32 pm #84244Dave,
To establish the VOP there are two primary statistics that drive us forward. We need sample estimates for the population parameters of central tendency and dispersion (we’ll stick with the assumption of normality for now). So, with that said there are a wide spectrum of tools available to establish, refine, and institutionalize our estimates of dispersion. If you have very low levels of process knowledge and need potentially a ‘quick and dirty’ first approximation we would prefer some estimate of dispersion from the voice of the process. One could use the average range of available data divided by 6 to come up with a first swag estimate. Will this be the Valhalla of dispersion? No. But that’s left for followon tools and really mapping and understanding the process.
Regards,
Erik0March 31, 2003 at 12:46 pm #84331Dave,
Draw 2 distributions in front of you 10,20,30,40,50 and 10,30,30,30,50 as you will see they both have the same range but are clearly not the same, Standard Deviation will pick this difference up.
Hope this helps0March 31, 2003 at 2:21 pm #84334
Andrew M. BrodyParticipant@AndrewM.Brody Include @AndrewM.Brody in your post and this person will
be notified via email.Just because 68% of the data points fall within +/ 1 Std. Dev.does not define what that 1 std. dev. is. All you have is an estimation at least as I read your statement. I may have missed your point totally for which I apologize.
Andrew M. Brody0April 1, 2003 at 9:02 pm #84405
GabrielParticipant@Gabriel Include @Gabriel in your post and this person will
be notified via email.“How would others have replied?”
I would have replied:
– Uh!?!? How do you derive “use 33% of the range to give you a value for standard deviation” from “68% of data was within +/1 std devs”? I just don’t see the link between both statements.
Yet, some points can be remarked.
– You were in an SPC training. Were you talking about the XbarR charts? In this context, R is a parameter of each subgroup, and each subgroup has its own R. If you have, let’s say 30 subgroups, which R do you use to take that “33%” for the stdev value? Will you get a stdev for each subgroup? Will you use Rbar (not R). Will you use the range between the max and the min of all measurements in all subgroups?
– In any case, note that any of the above ranges will increase as the sample size increases. Imagine a normal distribution with a given standard deviation. If you take only 2 parts it is unlikely that you will have any of them far in the tails. Then the range will be (on average) small. If you take 1000 parts it is very probable that you will have at least 1 part far in one tail and at least 1 part far in the opposite tail, then the range will be (on average) large. The range increased (and of course also the 33% of the range increased). Did the stdev increased? Absolutely not.
– Yet, there is a direct relation (proportional) between the stdev of a distribution and the range you will get (on average) from samples of size n taken from that distribution. If it is a normal distribution, that relation is d2, and there you get Rbar=d2*sigma. I guess this is the “all the calculations” you were asked about.0 
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