A Standard Deviation Primer with Picture

M

markr6754

New member
The attached photo depicts normal distribution (Bell Curve) data. There are 143 bullets pictured, ranging from 113.8gr to 116.2gr. The mean (average) is 114.90699, though you’ll agree that no single bullet is likely to weigh exactly at the mean. The mode is 115...this is another type of average, and merely indicates which bullet weight appears most often (21 times).

The standard deviation is 0.43761. This means that 68% (97.25) of the bullets will range between 115.3446gr and 114.46938gr. Counting them out you’ll find that 89 bullets lie between 115.3gr and 114.5gr, so the remaining 8.25 bullets are either 115.4gr or 114.4gr.

https://thefiringline.com/forums/attachment.php?attachmentid=108198&d=1536628850

Just another public service from someone new to reloading, but highly schooled in statistics.
 
Ruga Booga said:
Is there a point to this or is this just for informational purposes?
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I’m of the opinion that many reloaders don’t understand what standard deviation means, or how one would interpret the data when results and sd are provided. Thought a picture with an explanation, but without all the formulas and calculations may prove useful to some, but not all.
 
I like the way you presented it. I "get" math, but that makes it so you can visually take in the info. Thank you.
 
The problem with standard deviation as applied to reloading and shooting is that in practice, you are stuck with the extreme spread. Or are you going to discard 32% of those rather low quality bullets because they are not within one SD?
 
When it cones to reloading, the most important standard deviation to me is in group size and accuracy, especially when it comes to handgun ammo.

Everything else is just window dressing.
 
SD can be defined in one word - consistency

and it really only applicable to rifle accuracy at 500+ yards. I have a .223 load that shoots .5 MOA 5- 10 shot groups at 300 yards with a SD in the mid 30's and a ES of 90. If I shot it at 600 the vertical spread from velocity alone would be 1 MOA assuming my hold was perfect for each shot
 
I'd be okay with that for a handgun bullet, but further sorting would be necessary if I was serious and the sample was a rifle bullet. (Or a handgun bullet used in a rifle for serious purposes.)



Consistency is beauty.
This one surprised the hell out of me:

attachment.php

(These were sorted because they were blems. Original post: Beer + time + 1,000 Hornady SSTs + electronic scale = A chart!)
 
FrankenMauser said:
I'd be okay with that for a handgun bullet, but further sorting would be necessary if I was serious and the sample was a rifle bullet. (Or a handgun bullet used in a rifle for serious purposes.)



Consistency is beauty.
This one surprised the hell out of me:

attachment.php

(These were sorted because they were blems. Original post: Beer + time + 1,000 Hornady SSTs + electronic scale = A chart!)
Click to expand...
That is an amazing data set! Totally agree with the Handgun vs Rifle issue. Although I did ultimately separate and package the bullets by weight, so as to not waste my effort, the real purpose of my post was to illustrate normally distributed data, calculation of mean and mode and what sd means.

For most readers of the forum, this will help to compare performance data, as projectile velocity for a given load will tend to normally distributed data...and hence the value of knowing how sd comes to play.
 
Good illustration. As another statistics person, I’m curious about the two minor peaks. It may indicate they’ve got multiple production lines that are slightly different. I’ve done the same thing on a smaller scale. That was also my great grandfather’s rifle accuracy trick back in the 1920s and 30s was to buy cheap bulk bullets and group them by smaller weight groups.
 
hounddawg said:
SD can be defined in one word - consistency
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So can extreme spread. I'm much more interested in controlling my extreme spread than I am about what the standard deviation is. Standard deviation is a mathematical concept, but a few unusually slow or fast rounds I can hear and feel -- and possibly see on the target.
 
tmd47762 said:
That was also my great grandfather’s rifle accuracy trick back in the 1920s and 30s was to buy cheap bulk bullets and group them by smaller weight groups.
Click to expand...
I know a competitive bullseye shooter who does that.
 
That photo didn't tell me anything . In fact it actually makes it harder to understand what the likelihood one shot will be to the next


Example

It appears to say you are much more likely to get 115.4 & 114.7 then you are 115.3 or 115.2 . Why would that be more likely in reloading and your velocities ? I've shown how you hold the rifle effects your ES/SD quite a bit while using the exact same load loaded at the same time with all the same lot components . That was with rifle but I've done it with pistol and extreme limp wristing and death grip holds changed the velocities and ES/SD .

This is not a straight numbers game and why I asked about the ES in that other thread . When you're not the one running the test and don't have all the data . You have no idea if there were other inconsistencies that may have caused those differences . Sure you can extrapolate the likely hood of something but it's not the same as having the actual data .
 
markr6754 said:
6 sigma Black Belt.
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....and this is relevant, how?

Maybe to say we should spend a tad more for better quality bullets or that we get what we pay for when it comes to cheap bulk bullets? Maybe the comptroller for whoever makes those FMJs for Everglades is also a Black Belt and has come to the conclusion, that the most profit is to be made at the level of quality and the price point offered, eh?

I would tend to think with a "6 sigma Black Belt" mentality, you would realize that "Although I did ultimately separate and package the bullets by weight, so as to not waste my effort" due to the inherent accuracy of 9mm platforms, the short distances that 9mm is normally shot at and the fact that most 9mm handloaders use a powder thrower, that the separation was most likely, indeed a waste of your effort. Maybe just the "new to reloading" in you,eh?

Not trying to be an azz, just that most of us that have reloaded for a while, do not need to be patronized and given a 3rd grade example of standard deviation, with the implication we need it, in order to understand it.
 
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