Brent et al;
I love the range. The calculated standard deviation from a sample of data is an estimate of the population SD. The range, corrected for bias, is also an estimator of SD.
One may use either estimate of SD in any calculation.
On your targets; 3 and 5 are round looking groups, 2,6 and 8 are not. I don't think that we can say that the process is in or out of control based on 5 shots = 1 group. Statements about control maybe need 5 groups or so for validity. What I will tell you is that if those targets were shot with the same equipment/load in about the same conditions, then the shooting process is out of control and something other than statistics needs to be done.
I don't dislike statistical analysis, don't  think I know it all (Anybody who thinks they do should look at "Bias in Mental Testing" by Herrnstein?).
Have at it, enjoy yourself, I was once a true believer myself, and I know how it feels to be able to change the world. 
Did you look at the Ed Wosika stuff?
joe b.

Well, Brent, I'd refer you to 
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or
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or search on "range standard deviation"
or 
control chart
or statistical process control
The range has been used as an estimator of SD since at least 1931, when Shewhart sort of invented SPC.
When I entered graduate school (Economics, MA, 1972, Northeastern University, Boston, MA) several math and stat teachers balked, as you did-saying it ain't so. About 10 minutes with "Statistical Quality Control" by Grant, now Grant & Leavenworth last I looked, boogered their minds. 
Quality and Statistical Process Control
Here's a little info:
Prof. Sid Sytsma – Ferris State University
Statistical Process Control 

"Shewhart's discovery statistical process control or SPC, is a methodology for charting the process and quickly determining when a process is "out of control" (e.g., a special cause variation is present because something unusual is occurring in the process)."
A few minutes on the computer will explain all about using the RANGE as an estimator of SD, and what "in control" and "out of control" mean. 
Perhaps, Brent, you don't know quite everything that you think you know?
Look it up, Brent, do the work
joe b.

JoeB;

>>>Perhaps, Brent, you don't know quite everything that you think you know? 
Look it up, Brent, do the work 
joe b. <<<

Disagree all you want. You do NOT have to insult everyone who disagrees with you. You nearly ruined the last forum before you were removed. How about "chilling down" a bit?

You and others have a lot to contribute. We need this forum to remain civil for ALL of our benefits.

R. Dale McGee

Perhaps my manner is offensive. When I read that "The range is NEVER...", that is kind of offensive. I used and taught SPC/SQC for 40 years, and telling me that it ain't just gets me riled up.
As I said when I entered the fray, my interest is in the variability of group size.
For instance, Pete says that his rifle shoots into 9/16" for 5 shots at 100 yards on a quiet day. 
I don't know what he means by that. 
Is this the best group, or 1 in 5, or an average, or what?
In 2002 at the CBA Nationals, for an average of 4 five shot 100 yard groups, one of 41 shooters shot less than 9/16" = .5625", and only 4 shot under .6"
In 2003 4 of 49 shooters averaged under .6".
I record group sizes for every group shot. I find that my groups vary widely from group to group on the same day, and from day to day with identical loads, and they seem to get smaller the more I shoot on any given day.
In the 1997 Handloaders Digest, "Let's put some numbers on accuracy" by Paul Schiffelbein, PhD  says that 185 five shot groups are required to get a variability estimate that is good to within +/- 5%.
Maybe this is true, I hope not. My shift from IMR4227 to AA#9 in my Martini 30/30 bench gun was driven by far fewer groups, although the question was slightly different.
My query is kind of f-testy, variation within the data vs. variation between the data. If my gun shoots from .25" to 1.25"  over a long run, is that to be expected or is something wrong?
I hope that this hasn't been overly offensive.
When is the next ASSRA Journal coming?
joe b.

joe b.,

"For instance, Pete says that his rifle shoots into 9/16" for 5 shots at 100 yards on a quiet day.  
I don't know what he means by that."

 Ok... I can see I need to be a little more specific for you. So here are the last ten group sizes.

3/4" - 5/8" - 9/16" - 9/16" - 9/16" - 7/8" - 1/2" - 11/16" - 3/8" - 9/16".

 Out of these ten I would say only two are "round". The rest have at least one shot that at least increases the group by half.

 Of course, in my opinion these mean nothing without the conditions they were shot under. No more than one of these groups was shot on any given day, as I was using this load as a control for other testing. The smaller groups all were shot under "ideal" conditions. 7 AM in the morning, dead calm, target and ground in shade with no sign of mirage. The larger groups were shot on days at about the same time but some wind was present, varying from 7 to 3 o'clock depending on the day. The same condition was tried for but I can't say I hit it exactly every time.

 Since I shoot every day I don't record every shot, but do keep the targets till I have decided that a particular load combo is the best or not worth pursuing. But I do agree with you that groups will vary within the same day, and day to day. When you reach a certain level with you gun/load you need some way of confirming that it is the best load. This is where I think some math program would be of benefit.

 Both GWarden and myself are both having a hard time figuring out whether..... in my case a 1-25 or 1-30 alloy is best, and GWarden has the same problem with 1-20, & 1-25. What we need is something SIMPLE that can tell us over a fairly decent interval of shooting which would be the best. Both of us, I think have fired enuf of each alloy that we should be able to tell, but one day one will be better, and the next the other. Seems like we can go on forever like this and not be able to decide.

PETE

P.S.  Since Brent is a personal friend of mine I won't get into who's manner is most offensive. I'll only say that it's not how you perceive yourself, it's how others perceive you that counts. Both of you should state your case and leave the personalities out!

Ah, another great weekend in the books only to return to this sort of junk.   

Joe, 
If you don't like it, don't go there.  It is as simple as that.  If you want to hang on to range rather than SDs as an estimate of SDs - great.  More power to ya.  But it won't fly anywhere in any science I'm familiar with.  It surely won't get you published in my field.  If you wish to bandy about references and qualification on traditional and universally accepted statistical techniques, I have on my shelf right now,...

Design and Analysis of Experiments by John Gill.  I spent an entire year in Gill's courses (3 volumes).   

Then there is another perennial favorite, Sokal and Rolf's Biometery - about 850 pages of quite basic traditional statistics, 

And, let's see, Conover's Practical Nonparameterics -another semester spent on dissecting that.  Nonparameterics could be a quick good fix to the lack of statistical rigor in shooting.  But then you would see that immediately.   

There were several course in multivariate statistics that I spent my time (and money) in.  No texts handy, but multivariate stats would be an interesting way to go for a lot of load development, but no way that I know to make it easy for the average shooter.  Oh wait, yes, Multivariate Statstical Methods by Manly.  And a couple devoted to the arcane field of community ecology that would have little utility here.   

Then, lest we dwell on just the applied stats, I spent a year working through Hogg and Craig's Introduction to Mathematical Statistics, deriving the theoretical underpinnings of stastitical methology and probability theory.  Worked under Larry Shear on this.  he is fairly intense and more than slightly competent by most standards (standards of statisticians, not rank amatures like me).

And last of the general theoretical stastictics books, Noel Cressie's Statistics for Spatial Data.  Noel was/is pretty much a spatial stats diety.  He makes Larry look like milk toast for breakfast.  I spent a semester with him and a dozen of his and other Stats PhD students learning how to work with spatially organized data.  Application of spatial stats to shooting would be an interesting idea since a group on a target is nothing less than a map of events in space and time, but point-process analyses, or some sort of cludged variogram/kriging technique might be a whole lot more work than it's worth.  It would be great, I think, for diagnosing an potentially busted scope however, and probably other things as well.

None of these, btw, rely on range or semi-interquartile range to do anything useful.   

So, there you have it.  My "library" as it were (and is) and my background.  For an ecologist, I'm probably in the middle of the pack with respect to using stats, but a good bit ahead of the pack with respect to statistical training.  I'm surely no professional statistician, but I play with them (professional statisticians every day  

So, I'll stick with that.  Something like 10 courses in statistical training and 25+ years of doing it is quite enough to get me down the road to better shooting analyses. 

End Part I   
Brent

  Good! I'm glad we're movin' on.

  Three of us had a little fun with this... at Brent's expense this past weekend..... which is why he's probably a little owly today! 

  Without boring you with the details todays shooting really pointed up the "out of control", or the more commonly called "flyer". Some of the groups were REALLY out of control and it was interesting, with our messages on this as witness, that the really bad shots would show up on the chronograph with big changes in MV's, and a final large SD/ES.

  But.... All these would have been pretty obvious without the chronograph data.

  I had one tho that would have had some thinking maybe there was something wrong with that bullet. The group was 2 1/8", with 4 in 15/16". Without the chronograph I would probably fire this a coupla more times to see if that " flyer" was just a fluke shot. But the chronograph showed that altho the MV averaged in that sweet spot of around 1405 fps, the SD was 33.9 and the ES was 90.3. Since I know with this gun I need to get the SD's below 10, I can pretty safely say this load isn't worth expending anymore time on.

  To me it's cases like these that make Statistical Analysis a shortcut to finding the best load.

  But, what's really needed is something that can take a series of tests, with nearly identical results, and compare them to see which is best, such as I mentioned where I was having trouble determining whether 1-25 or 1-30 was the best alloy to use. Something that doesn't take a rocket scientist to apply.

  To me this is why I don't think SA is a practical option for most people to use. Taking the group above as an example, if I didn't have a chronograph it would have been a lot easier for me to just fire a coupla more groups to get the answer rather than to spend hours(?) using SA to come up with an answer, IF I even understood which part of SA to use in the first place. What we need is a better mousetrap!

PETE