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Old September 11, 2018, 08:03 PM   #1
markr6754
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A Standard Deviation Primer with Picture

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/att...8&d=1536628850

Just another public service from someone new to reloading, but highly schooled in statistics.
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Old September 11, 2018, 10:11 PM   #2
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Is there a point to this or is this just for informational purposes?
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Old September 12, 2018, 12:51 AM   #3
markr6754
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Originally Posted by Ruga Booga View Post
Is there a point to this or is this just for informational purposes?
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.
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Old September 12, 2018, 06:43 AM   #4
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I like the way you presented it. I "get" math, but that makes it so you can visually take in the info. Thank you.
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Old September 12, 2018, 08:13 AM   #5
Jim Watson
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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?
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Old September 12, 2018, 08:29 AM   #6
buck460XVR
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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.
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Old September 12, 2018, 09:00 AM   #7
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What buck460XVR said. You can have somewhat higher SD, but, very accurate loads.
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Old September 12, 2018, 09:29 AM   #8
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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
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Old September 12, 2018, 12:07 PM   #9
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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:


(These were sorted because they were blems. Original post: Beer + time + 1,000 Hornady SSTs + electronic scale = A chart!)
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Old September 12, 2018, 04:59 PM   #10
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Markr6754:
Many thanks for the info. Interesting data & many thanks for posting.

Last edited by Gary Wells; September 12, 2018 at 05:16 PM.
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Old September 12, 2018, 08:39 PM   #11
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Originally Posted by FrankenMauser View Post
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:


(These were sorted because they were blems. Original post: Beer + time + 1,000 Hornady SSTs + electronic scale = A chart!)
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.
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Old September 12, 2018, 08:45 PM   #12
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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.
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Old September 12, 2018, 09:57 PM   #13
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Originally Posted by markr6754 View Post

Just another public service from someone new to reloading, but highly schooled in statistics.
How highly schooled?
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Old September 12, 2018, 10:10 PM   #14
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Originally Posted by hounddawg
SD can be defined in one word - consistency
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.
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Old September 12, 2018, 10:12 PM   #15
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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.
I know a competitive bullseye shooter who does that.
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Old September 12, 2018, 10:42 PM   #16
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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 .
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Old September 12, 2018, 11:07 PM   #17
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How highly schooled?
6 sigma Black Belt. Ohio Award for Excellence Examiner. Summa Cum Laude in Accounting.
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Old September 12, 2018, 11:14 PM   #18
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6 sigma Black Belt. Ohio Award for Excellence Examiner. Summa Cum Laude in Accounting.
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Yea but can you kick my , WHAAAAT -
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Old September 12, 2018, 11:26 PM   #19
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The problem with statistics is that there is always an unexplained outlier.
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Old September 13, 2018, 08:32 AM   #20
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Originally Posted by markr6754 View Post
6 sigma Black Belt.
....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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Old September 13, 2018, 09:00 AM   #21
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I like the picture, works for me.
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Old September 13, 2018, 04:22 PM   #22
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Ten years from now (or sooner) another new reloader with a black belt in number crunching will make a similar post with a similar pic and similar explanation for the unwashed masses and you'll go, "Yeah, whatever."
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Old September 13, 2018, 04:48 PM   #23
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Guys...this post wasn't made to piss anyone off. I got new bullets, I had never used them before. I was curious how close they came to 115gr and started weighing them. As I've never weighed out a box of bullets before I was surprised at the rather extreme (to me) spreads, but also noticed that this was "Normally Distributed" data, and thought it would be a good use to determine the sd, mean, mode, and etc. Now, I had been challenged in another thread about my use of sd, so of course I thought I'd share what I'd already been working on since last Friday.

It wasn't my intent to throw my credentials in anyone's face...I responded to a specific questions from 74A95.

Clearly I made some angry, pleased others, and came off looking like an a$$...I do apologize. As a new reloader I thought I had something helpful to share...but I missed the mark.

I'd like to apologize openly to higgite, buck460xvr, Metal God, Jim Watson, Ruga Booga, Aguila Blanca, and anyone else that I antagonized. Really, I'm not an a$$, though I may have come off like one. You guys have all provided value to me since I came to this site in February, along with many others. Thanks for your patience, and pardon...should you offer it.
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Old September 13, 2018, 04:59 PM   #24
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I don't see where the OP did anything to apologize for, this thread sure beats the unsolvable "help me I have fallen and can't reach my bench" threads.

Only thing I would criticize here this is what I criticize on most weighing thread is if you are not using a scale that is capable of .0001 grams you are spinning your wheels. If your measurements were done on a typical .1 gn scale the readings are subject to a = or - .1 error.
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Old September 13, 2018, 10:28 PM   #25
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Thanks for the apology but that is not necessary , really . It takes quite a bit to upset me and the mods on here tend to stop any dialog way before anyone gets me mad . My point in this thread and the other was simply . When talking SD in relation to firearms velocity , it's not just a straight numbers game . As I pointed out earlier , just how you hold the firearm can effect those numbers . There are many variables that effect velocities and there consistency . This is why I saw nothing in your bullet example that really related to the other thread . Your bullet weight SD sheet was really only dependent on the quality of your scale as the number one variable . Everything else is fixed and can't be changed . While internal/external ballistics are dependent on the constancy of the charge , primer seating , bullet , neck tension , firearm hold etc etc etc . Which is all dependent on a human

This is why in firearms the SD IMO is best described as what the likely difference will be from one shot to the next . Although your bullet graph is interesting It does not really tell me what the likelihood one bullet will weigh compared to the next with out doing more math , therefore not that helpful to me . You did bring up this was so we could understand SD as it relates to the other thread or at least that's how I read that . I'm no math beautician but in my head your bullet chart does not help me understand velocity SD's . I'm open for some learning if you can help explain how it relates ?? or anyone else for that matter ?

Regardless let me thank you for even doing that bullet test . I do my fare share of testing and posting of results on this and other forums . Sometimes I feel people don't get the time involved to do some of the testing and then post the results . Be sure that I at least understand the effort you made and appreciate it none the less .
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Last edited by Metal god; September 14, 2018 at 10:40 AM.
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