Easy way to figure standard deviation

[gray wolf]

If you have a chronograph that does not figure standard deviation, here is a very easy calculator that will do the math for you. Put in your numbers separated by a , and hit calculate.

http://www.calculator.net/standard-deviation-calculator.html?numberinputs=800%2C801%2C810%2C820&x=43&y=6

[Walter Laich]

I like it! Now to bookmark it for later--I'm known for not doing this and hating myself afterwards

[engineer401]

I bookmarked this page. Statistics class was required for my engineering degree. The lectures were long and slow. Thank you for the website.

[mrbill2]

Well I be damned even a pregnancy calculator. What more do we need. THANKS

[dverna]

Almost as easy to use Excel, and then you can save the file and have a record - along with other info you may wish to save.

Don Verna

[imashooter2]

Almost as easy to use Excel, and then you can save the file and have a record - along with other info you may wish to save.

Don Verna

http://mywebpages.comcast.net/imashooter2/crnycalc.xls

Input 2 to 20 shots and bullet weight. Output High, Low, Average, Extreme Spread, Standard Deviation, Kinetic Energy and Power Factor

[williamwaco]

Thanks for sharing that.

I think it is a great idea.

[MtGun44]

I remember from statistics class that for sample sizes smaller than about 30 or 40 or
so SD is not very accurate.

[imashooter2]

I am not a trained statistician, but when I was making my spread sheet, this is what I found on the net:

The percentage error decreases roughly like the inverse square root of the sample size, which is not that fast.

Sample Size \ Percentage Error to be expected
2 \ 60%
3 \ 46%
4 \ 39%
10 \ 23%
20 \ 16%
30 \ 13%
50 \ 10%
100 \ 7%
200 \ 5%
800 \ 2.5%
5000 \ 1%


Personally, I'm good with 10 samples and more than 20 seemed like wasted effort (hence the limit in my sheet).

[Scharfschuetze]

Thanks for that link!

Like many others, statistics in college was a "challenge" for me. Glad I got through it though and the Tests and Measurements course was also of value. I must admit though, that after that particular semester, I took the book out to the country side and used it for a target! Wish I had the book now. Oh well...

When testing target rifle loads for accuracy and ballistic uniformity, I usually use 10 shot strings for testing. As noted above, more than that is just wearing out an expensive barrel.

[leftiye]

Yup, statistics in college, is where it belongs. This is a johnny come lately thang. Never need it (did know how, but kept it in the sosiology dept.) until lately. Groups count. It's just like people who think they can tell pressures by looking at a chronograph.

[MtGun44]

Your OK with 23% error?? IMO, that is a huge error.

I'll stand by the "less than 30 or 40 samples, SD is not very accurate." - by 50 it is down to 10% error,
starting to get there for me.

Bill

[Tatume]

At one time Federal Cartridge was very concerned that the Russians were using better 22 LR ammunition in Olympic events than the U.S. team. They set out to improve the Federal Gold Match ammunition line. My friend Don Rummler was one of the people contracted to test ammunition. He used the old wind tunnel at NASA/Langley in Hampton, VA for a test range. The test facility had four chronographs, two next to each other close to the muzzle, and a pair at the target. The pairs were for the comparison of speed at each location, to detect a failure of one chronograph, if it were to happen.

Don and I did an analysis of standard deviations, with the idea of predicting the number of shots necessary to produce a reliable standard deviation on velocity (sd). Using a Monte Carlo simulation we determined that fewer than 20 shots gave sd that was completely random. Reliability of the sd was near zero. More than 30 shots improved reliability, and 50 shots were required for complete dependability.

I no longer depend upon sd for a measure of uniformity in ammunition, as I cannot usually shoot enough shots in a session. Sometimes I shoot a string long enough, but not often.

Take care, Tom

[Tatume]

MtGun44 has exceeded his storage allotment and cannot receive PMs.

[imashooter2]

Your OK with 23% error?? IMO, that is a huge error.

I'll stand by the "less than 30 or 40 samples, SD is not very accurate." - by 50 it is down to 10% error,
starting to get there for me.

Bill

23% of 10 fps = 2.3 fps. Yeah, I'm fine with it. I have no issue with you taking as many samples as your heart desires though. :)

[gray wolf]

I think a little to much education may be showing, ( not a bad thing--but ) if we were in a scientific environment I am sure some number would be picked for standard deviation concerning specific needs.
Sure we can get as technical as we want, but practicality has to rear it's head at some point for the average shooter.
When was the last time you shot next to someone who said :
Hey I will be done in a few minutes, I have to shoot 50 more rounds over the Chrono for my Standard deviation test. But if your in a hurry to check your target i guess I can come back tomorrow EH.
It doesn't happen in the real world with most shooters.
Sides, how many shooters make sure they put a level on there chronographs to make sure it's plumb to the earth ? and then make sure there gun barrel is plumb with the chronograph.
Or shoot over the exact spot, or take a tape and measure the distance each time, How many folks take a sample weapon with ammunition of a known velocity and shoot to test the Chrono.
Or shoot under ideal lighting conditions ?
Like I said: sometimes to much know how comes in the wrong door and gets into the discussions.
But in any event some good points have been made, But I don't think I will tell anyone they are using there equipment wrong and getting false info if they don't shoot 50 or 100 rounds over there Chronograph. I think if most people followed these simple guide lines they would be ahead of the Chrono game.

http://precisionrifleblog.com/2012/07/20/chronograph-accuracy-tips-15-practical-tips-to-increase-accuracy-reliability/

[Tatume]

Hi Wolf,

Are you saying a wrong answer is better than a correct answer if it's easier?

Take care, Tom

[gray wolf]

Hi Wolf,

Are you saying a wrong answer is better than a correct answer if it's easier?

Take care, Tom
WOW, talk about selective reading, To answer your question, no, I don't deal with wrong answers.
My post was to just state the practicality of fireing many shots for the average shooter.
Sometimes I think we need a pick and chat section, that way we can pick apart a post and choose what part to chat about.

[Tatume]

Speaking of selective reading, please note that I never advocated the casual shooter firing strings of 50 shots for velocity. I said that shooting short strings does not give a useful sd. That doesn't mean the average velocity is worthless, just the sd.

In our case we were being paid to make a determination about the consistancy of velocity for a major manufacturer. We fired an entire lot of ammo! When we were done we knew the population standard deviation of velocity for that lot, and were able to come to substantial conclusions about the lot of ammo, and about subsets of the lot. It was from the subsets that we came to our conclusion about sd on small samples, since we had the actual population sd to which we could compare the sample sd.

[gray wolf]

Sir you do not have to defend what you did or what you said, no one is picking on you, relax.
and BTW, thank you for your post and your Up-date, i found in interesting, and food for thought and that is a fact.

[popper]

Or you could use Excel to plot a histogram and visually look at the results to see if your load is really good. Political polls use the 23% numbers, right?

[Scharfschuetze]

Yes, I'm very comfortable with 10 shot groups or that 23% error. I guess it's all about what your shooting goals are. If you are hunting, match shooting, plinking or just shooting to enjoy reloading, your needs are going to be different.

Most of my match loads for national match as well as long range matches have had on average a SD of around 12 to 15 with weighed cases and match bullets. Some lots of powder actually will refine to a SD of 10 or so. When I develop a load, I shoot 10 shot groups of each powder charge within the testing regime for each bullet brand or weight. That is a total of about 60 shots for any given bullet for about six different charge levels. That can add up to several hundred rounds when developing a load for a new barrel when using different powders, cases, primers and bullets. I then graph the results to determine powder efficiency per grain of powder, the extreme spread and the standard deviation and then compare the results against the 10 shot groups made at 200 yards for each change in components. Now a good match barrel in 7.62 NATO/308 Winchester will generally last, on average, about four to five thousand rounds (some more, some less) and remain competitive at the master or high master levels of competition. The really high performance rounds like the 6.5mm/284 will wear an expensive barrel out in about two thrids of those numbers. Would you rather wear a barrel out finding out what charge it likes to the nth degree or would you rather use it? Factor in the current costs of match bullets, powder, good cases and primers and... Well, you can do the math.

With the above effort, I'm pretty sure that a 23% error of a SD of 10 or 12 is pretty inconsequential. I can live with that and to be honest, I don't think that I any rifle I have or any target I've shot at could tell the difference.

[MtGun44]

IMO, SD is pretty much useless for shooting when doing small batches. Not particualarly
accurate, doesn't tell you much useful.

Bill

[popper]

As the posts show, SD is valuable in determining the quality of the 'load' but is difficult to get. A simple plot of shot velocity will tell you exactly what you need to know.

[Bullwolf]

I've have a simple inexpensive chronograph that doesn't give a print out with the SD or a FPS average. Because of that, I have just been using an online average calculator for my notes.

I bookmarked the link, and I like it better than what I was previously using.

Thank you for posting that.



- Bullwolf

[beagle]

I keep my data on an Excel spreadsheet for rifle loads and a separate sheet for pistol loads. At the top of each I have set up an expandable model that allows me to plug in velocities (expandable to any amount of entries). It automatically calculates the average velocity and the SD of whatever I enter. Then a simple matter to record it in my spreadsheet./beagle

[Scharfschuetze]

A small SD is not critical for plinking ammo, but for ammo that performs predictably at extended ranges it is worth the effort to find it in combination with a load that groups well.

Once I settle on a load, I'll use it until the components are gone and that can be the life of a barrel for a match rifle. Predictable performance at long range on small targets or in difficult conditions is well worth the effort. While this means buying components in bulk for a match season, in the end it is worth the expense in reduced frustration and constant load testing.

I'm currently preparing for an extended trip to my home state in the Rocky Mountains and will spend a couple of weeks shooting various firearms and prairie dog hunting with my .223 bolt rifle. This year a stash of 60 grain Hornady V-Max bullets to buck the afternoon winds at ranges out past 300 yards will get loaded. Needless to say, the Dillon 550 press will be working overtime to prepare the number of prairie dog rounds needed for the trip after I establish the best load, covering all the bases, for this bullet in this rifle.

PS. I realize that this is the "cast boolit" forum, so forgive my examples using jacketed bullets. I test pretty much the same way with cast boolits, so I guess it isn't too far off top as once I find a good cast boolit load for a rifle I then standardize on it too trying to keep all components the same for as long as possible.