Standard Deviation

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Standard Deviation

Postby Jim in Houston » Thu Oct 11, 2012 12:17 pm

Gun Tests Magazine just did a good write-up on on their protocol for testing ammunition. Although they were primarily looking at ammo for self defense, I thought their explanation of standard deviation was especially good:

    Of these two measurements, extreme spread and standard deviation, the latter is by far the most important. It's also a measurement not fully understood by many people, thus not often used by non-professionals. This is unfortunate because it's the single most meaningful measurement of velocity results. The mathematical equation used to determine standard deviation is extremely complex, and prior to the existence of computers was seldom used by shooters. Fortunately, these days many chronographs, including the CED Millennium, will calculate standard deviation for you at the push of a button.

    Standard deviation tells you how close you can expect the velocity of any shot you fire to be to the average velocity. Statistically, it's been proven that 99.7 percent of rounds fired will fall within three standard deviations above or below the average velocity. 95.4 percent will fall within two standard deviations above or below. And 68 percent will fall within one standard deviation above or below. For example, if our 20 shots generate an average velocity of 1,000 fps with a standard deviation of 10, we can bet the farm that almost every round of that ammo we fire out of that gun (99.7 percent) will fall between 970 and 1,030 fps. Similarly, 95.4 percent will be between 980 and 1,020 fps. And 68 percent will be between 990 and 1,010 fps. Now that's some meaningful data.

    A small standard deviation is always a sign of ammunition that's been assembled with skill and attention to detail. By the same token, a wide standard deviation can usually be taken as an indictment of quality control. The more consistent the ammunition, the better the odds it will produce the exact same result, both in accuracy and terminally, every time.


As has been mentioned in this forum for the 450 BM, SD's appear to be fairly large and difficult to get lower, regardless of how much care we take in reloading.

The whole article is at http://www.gunreports.com/special_reports/ammo/Gun-Tests-Ammunition-Testing-Winchester-Cor-Bon-Remington-Black-Hills1895-1.html?ET=gunreports:e1295:138145a:&st=email.
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Re: Standard Deviation

Postby commander faschisto » Thu Oct 11, 2012 12:37 pm

Very good explanation, even though it still makes my head hurt....I'm sure WC will have some insight on this to share concerning the 450b?
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Re: Standard Deviation

Postby wildcatter » Sat Oct 13, 2012 5:16 pm

Jim in Houston wrote:Gun Tests Magazine just did a good write-up on on their protocol for testing ammunition. Although they were primarily looking at ammo for self defense, I thought their explanation of standard deviation was especially good:

    Of these two measurements, extreme spread and "STANDARD-DEVIATION", the latter is by far the most important. It's also a measurement not fully understood by many people, thus not often used by non-professionals. This is unfortunate because it's the "Is the Single Most Meaningful Measurement of VELOCITY-RESULTS" (WC's Editorial Emphasis). The mathematical equation used to determine standard deviation is extremely complex, and prior to the existence of computers was seldom used by shooters. Fortunately, these days many chronographs, including the CED Millennium, will calculate standard deviation for you at the push of a button.

    Standard deviation tells you how close you can expect the velocity of any shot you fire to be to the average velocity. Statistically, it's been proven that 99.7 percent of rounds fired will fall within three standard deviations above or below the average velocity. 95.4 percent will fall within two standard deviations above or below. And 68 percent will fall within one standard deviation above or below. For example, if our 20 shots generate an average velocity of 1,000 fps with a standard deviation of 10, we can bet the farm that almost every round of that ammo we fire out of that gun (99.7 percent) will fall between 970 and 1,030 fps. Similarly, 95.4 percent will be between 980 and 1,020 fps. And 68 percent will be between 990 and 1,010 fps. Now that's some meaningful data.

    A small standard deviation is always a sign of ammunition that's been assembled with skill and attention to detail. By the same token, a wide standard deviation can usually be taken as an indictment of quality control. The more consistent the ammunition, the better the odds it will produce the exact same result, both in accuracy and terminally, every time.


As has been mentioned in this forum for the 450 BM, SD's appear to be fairly large and difficult to get lower, regardless of how much care we take in reloading.

The whole article is at http://www.gunreports.com/special_reports/ammo/Gun-Tests-Ammunition-Testing-Winchester-Cor-Bon-Remington-Black-Hills1895-1.html?ET=gunreports:e1295:138145a:&st=email.


All that Voodoo is absolutely true, but the most accurate loads I've tested, all had higher SD's. I bet Hoot has seen this Phenomenon, as well. I can't really explane it but it's sometimes true.

So then, this article, is the very reason I use loads with Zero (0) Velocity SD's. While you are scratching your heads on the statement "ZERO", how is that possible?? Let me explane.

A 100rd group will have a much better SD than a five rd group, usually. The larger the sampling the better the results, usually.

However, the way I always achieve ZERO SD's, is to have two chronographs, Co-Phased, so that their read-out are exactly the same. By placing one up at the weapon and the other out at the 200yd butts, each individual fired bullet will "Always" deliver a Zero SD, perfect BC numbers, and really kick-up the data flow Intel. So, no matter how many are fired in a string, I know exactly the average of that particular group.

Case in point.. Say you roll up 5000rds of a particular rd and shoot the first ten rounds with a SD of "X". The last ten rounds will have an entirely different SD. Even if you were to fire the first 30 rounds, in three ten round strings, and then average them against the last 30 rounds, fired and averaged, the same way, the SD's will still be different. "BUT", if I do the same 60 rounds, done the same way, I still get a SD of Zero for the first and last groups, get it or am I over the top again??

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Re: Standard Deviation

Postby Hoot » Sun Oct 14, 2012 7:47 am

I shouldn't have stayed up so late processing spent 30-06 first fires. Image

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Re: Standard Deviation

Postby Jim in Houston » Sun Oct 14, 2012 2:38 pm

WC makes my head hurt.
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Re: Standard Deviation

Postby Texas Sheepdawg » Sun Oct 14, 2012 5:03 pm

Now I know how I sound to the guys at work who periodically tell me that I spend way too much time smelling gunpowder.... But then, the most scientific they get around guns is debating Bud Light or Jack Daniels... I probably make their heads spin. :lol:
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Re: Standard Deviation

Postby Texas Sheepdawg » Sun Oct 14, 2012 5:05 pm

Jim in Houston wrote:WC makes my head hurt.

...And Hey Jim, You are the one who pulled his string! LOL!
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Re: Standard Deviation

Postby pitted bore » Sun Oct 28, 2012 8:02 pm

t-
Actually, with a single observation, the sample standard deviation is not zero; it is undefined.

Here's a link to the wikipedia discussion of standard deviation:
http://en.wikipedia.org/wiki/Standard_deviation#Sample_standard_deviation

Note the last sentence in the paragraph discussing the correction for bias: " Additionally, if N = 1, then there is no indication of deviation from the mean, and standard deviation should therefore be undefined."

You're procedure in calculating ballistic coefficient is correct, if I understand what you're doing. You shoot a shot, record velocities near the muzzle and at 200 yards, and then find your estimate of the BC of the bullet based on those two readings. If you do this several times for the same bullet, you will have several estimates of the BC. From these several estimates (a sample) you can calculate an average BC, and also the standard deviation of the BC based on the sample.

The average BC found in this way is less biased, I think, than calculating the BC using the average of readings at the muzzle and at 200 yards.

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Re: Standard Deviation

Postby Jim in Houston » Mon Oct 29, 2012 1:12 pm

But isn't the BC very dependent on atmospheric / enviornmental conditions like temperature, altitude, humidity, etc? Not saying you can't measure the BC, but to get something you could compare to what you find in the literature, you would need to correct for these parameters. On the other hand, if the conditions that exist when you take your measurements are the ones you are likely to be hunting in, then that would be the BC to use when calculating rise or drop in a ballistic computer.

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Re: Standard Deviation

Postby wildcatter » Mon Oct 29, 2012 2:07 pm

pitted bore wrote:t-
Actually, with a single observation, the sample standard deviation is not zero; it is undefined.

Here's a link to the wikipedia discussion of standard deviation:
http://en.wikipedia.org/wiki/Standard_deviation#Sample_standard_deviation

Note the last sentence in the paragraph discussing the correction for bias: " Additionally, if N = 1, then there is no indication of deviation from the mean, and standard deviation should therefore be undefined."

You're procedure in calculating ballistic coefficient is correct, if I understand what you're doing. You shoot a shot, record velocities near the muzzle and at 200 yards, and then find your estimate of the BC of the bullet based on those two readings. If you do this several times for the same bullet, you will have several estimates of the BC. From these several estimates (a sample) you can calculate an average BC, and also the standard deviation of the BC based on the sample.

The average BC found in this way is less biased, I think, than calculating the BC using the average of readings at the muzzle and at 200 yards.

--Bob



Correct, but done my way N=0 not 1. So, sure my SD's are undefined, being that they do not deviate any-at-all from the Mean..

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