rgchristensen wrote on Mar 10^th, 2014 at 8:07pm:

I disagree.(I don't think he means variance, I think he means accuracy. RMS^2 = variance.) 
Group size does not just consider the widest two shots, but is the range, and the range is frequently used to estimate standard deviation; as in Cat whisperer's imaginary x bar and r charts.
Mean radius and group size are mathematically related such that if we know one we know-or can calculate-the other.
The root mean square deviation of a set of numbers is the standard deviation of that set, and is also mathematically related to group size such that if one is known the other can be calculated.
Mean radius and s.d. are essentially the same as group size, are difficult to understand, aren't commonly used, and to my mind are a bit pretentious.

Assume that variables, acting alone, cause groups of certain sizes. Powder charge variation alone might work so: +/- 0 grain = .1 moa group; +/- .1 gr = .25 moa; +/- .2 gr = .6 moa. 
Then there are group sizes for bullet weight variation and seating depth and powder lot and .... 
How do these variables/group sizes add?  
Let there be only 2 variables, shooter with 3moa group size and gun with 1 moa group size. Make a 3" paper disc and a 1" paper disc. Lay the 3" disc on the table, repeatedly drop the 1" disc on top of the 3" disc such that they touch. Sometimes we get a "snow man", a total group size of 3" +1" = 4", the maximum. Sometimes the 1" disc is all inside the 3" disc. total group size = 3", the minimum. Total group size varies between 3" and 4". The average total group size is sqrt (3 sqrd +1 sqrd)  = sqrt 10 = 3.16".

Psychobabble............


      Joe.

joeb33050 wrote on Mar 11^th, 2014 at 6:28am:


Thus......... more pschycobabble.........

joeb:
Mean radius, radial SD, and group size can be inferred from one another ONLY if you know the distribution.   Given that one can prove a Gaussian distribution (not easy, nor safe to assume), you can readily relate these quantities.   For other distributions, the math can get hairy.
Interesting parallels are found in the evaluation of shotgun patterns.

CHRIS
RGChristensen

Well Chris, I assume a normal distribution, as do many others. I think it's both a safe and reasonable assumption, and Karl agreed, last time we spoke. As for "mean radius", the assumption is the definition of the center location. And we know that there are quite a few different centers of n points. Aren't there?


rgchristensen wrote on Mar 11^th, 2014 at 10:11am:

The short answer is that if you can stay consistently inside the 20 ring you are shooting in the top 10% of shooters at any given match.

40 Rod