Home Forums Hunting & Shooting Ask The Gunwriters Formula for Standard Deviation

I have an older chronograph which does not have the standard deviation feature. I did have a fairly easy formula for this but somehow I lost or misplaced it. I Googled for the formula but it was a fairly complicated procedure. The one I had was fairly simple and I found it valuable in developing handloads for both pistol and rifle loads. Can anyone offer any help on this? I would sincerely appreciate it.

Thanks in advance.

Roundup

Why do you want to compute SD ?

Sorry I can't help with an easy formula. When I took Statistics in college it was pre-calculator days. Figuring sd was a PITA. Then they came out with calculators, viola, click a couple of buttons and you had it.
Buy a cheap calculator.

There are on-line calculators. Just Google 'Standard Deviation Calculators'

Your post suggests to me you aren't mathematically inclined, so I suggest buying a calculator that will allow you to enter a string of numbers and then have it do the calculation.

You may not want to do that though. Denton will probably chime in and give you a quickie formula that will estimate the SD about as well as the real formula does for small data sets.

How many shots will you use in one string?

I'm probably a little lazy in this regard, and I use 10 shot strings to get an indication of how the load is working out plus the chronograph results on velocity. It has been my personal experience that loads which don't vary much in velocity are more accurate. There are exceptions in my case... .222 Remington as an example.

1) subtract the average value from each measured value
2) square all the previous results in step one
3) add all the values found in step two together
4) divide this result by the number of measurements less one
5) take the square root of the result found in step 4.

Example; OV = Observed Velocity & AV = Average Velocity

Round.....Velocity.....(OV - AV).....(OV - AV)Squared
1.............2734.............0.................0
2.............2745.............11...............121
3.............2750.............16...............256
4.............2741.............7.................49
5.............2700............-34...............1156
Sum.........13670..............................1582

Average velocity= 2734

1) take the sum of the differences squared and divide by the number of rounds fired less one
1582 divided by (5-1) = 395.5

2) take the squared root of 395.5 = 19.8817 (20 standard deviation)

Hey!

I found it!

AT: calculator.net standard deviation

Just enter the string of numbers and punch "calculate"

Thanks

Roundup

Since you're sitting at a computer why not load all the velocities into an Excel Spreadsheet and compute? That way you have all the data in one place. Just remember to save the file elsewhere so WHEN the computer dies you'll have a copy.

From the chronograph thread:

Shooting 10 shots, subtracting the smallest from the largest, and dividing the result by 3 is a very good method. The alternative is to shoot 4 shots and divide by 2. There are rules for other sample sizes, but those are the two that are easy to remember. For small samples, this method is actually better in some respects than the sum of squares method.

The best answer is, get a real calculator or one that installs on your smart phone. Or get one of the ballistics calculators for smart phones. If you're super cheap, spreadsheets almost universally have a STDEV function.

With any small sample, your estimate of standard deviation will not be very precise, no matter which of the multiple calculation methods you choose.

I agree with with the method just described. If you are using less than 10 shots to find the Highest velocity - lowest velocity, then use the following divisors (instead of 3):

2 shots - 1.128
3 shots - 1.693
4 shots - 2.059
5 shots - 2.326
6 shots - 2.534
7 shots - 2.704
8 shots - 2.847
9 shots - 2.970

David


For those who care - the constants above assume that velocities are normally distributed.

I had to do the same and calling manual calculation of SD a PITA is a huge understatement!

So is waiting your turn in the stat lab to use the Friden or whatever calculators.

Chug-a-chug-a-chug.

Ah, the days of grad school!

We would have killed for a simple $5 calculator, had such an animal existed.

Paul

Yes, I am reminded of a well schooled friend who told me in the mid '70's, if the hand held calculators ever got to $100 to buy one quick. They would never get any lower.

I ignore SD, I want small ES.....

Without going and looking at my notes, I seem to remember that for 3-shot strings the SD was pretty close to one-half the extreme spread for the string. But being a non-long-range shooter, both are nothing more than numbers I right down to impress myself.

Sounds like love and marriage...

Or, just use a calculator!

I took several statistics courses in college (pre-electronic calculator days) and it was a bear to figure out. Now, just plug in the numbers and viola!