Standard Deviation

[keith jones]

I thought I understood what standard deviation until me and a buddy were talking about it at work tonight. Would someone care to explain it to me. The calculations, and knowing what is good or bad. If this has been asked I am sorry I looked found several things on it. Just not explained> Thanks guys

 

[Killshot44]

Google is your friend. There are lots of good samples and explanations.

This is from a company that produces ballistic software http://www.shootingsoftware.com/ftp/Perverse Nature of SD.pdf

Tons of links: standard deviation muzzle velocity - Google Search

I think of Standard Deviation as essentially the average amount that the average shot deviates from the average.

In simple terms:

You might have muzzle velocities of 2800, 2805, 2810, 2790 & 2800 for an average (mean) of 2801 and a standard deviation of 7.4162.

or, you might have muzzle velocities of 800, 2805, 2810, 2790 & 4800 for an average (mean) of 2801 but a standard deviation of 1414.23. Extreme example to be sure but it shows how average and SD differ.

Remember, too, that it's all about Sample Size. Most feel that a sample of at least 30 is required but few experienced reloaders go to that length - too much barrel life spent for little improvement in the basis of the calculations.

 

[Bob 964]

The Standard Deviation (SD) shows how much variation there is from the average. The standard bell curve represents a normal distribution of data. In a normal distribution, 68.2% of the recorded data points would be +/- 1 SD from the average. To illustrate, imagine a 100-shot group with an average velocity of 2700 FPS and an SD of 25 FPS. Of the 100 shots, 68 would be expected to have velocities 25 FPS above or below the average velocity of 2700 FPS. Roughly 68 of the 100 shots would, therefore, have velocities between 2675 FPS and 2725 FPS.

 

[keith jones]

Thanks guys much appreciated.

 

[former naval person]

However, to complicate the issue...most folks doing the workup take the chronograph reading to be absolute. Not so. The potential accuracy of the various chronographs vary, and not just brand to brand but unit to unit. What percent of accuracy does your unit claim...and can it be verified?

 

[Fuzzball]

IIRC, SD is the square root of the sum of the squares of the difference between each sample and the mean.

 

[EMorr]

IIRC, SD is the square root of the sum of the squares of the difference between each sample and the mean.

This is pretty much the method I was taught, however I was told to subtract 1 from the sum of the squares of the difference off of the mean before dividing by the number of shots and then finding the square root of that number. When I do that I get numbers a little different than what Killshot44 posted.

Using that method I come up with a SD of 6.62 for his first example sand 1264.92 for his second example.

I believe this is call the population standard deviation. Just learned a little more the SD numbers from Killshot44 posted would be would be an example of Sample standard deviation, meaning that is the SD of those 5 numbers assuming they were picked from a larger group of numbers or velocities.

 

[keith jones]

What numbers are good numbers? How do you know whats good or bad? Thanks good info guys finding very helpful

 

[EMorr]

What numbers are good numbers? How do you know whats good or bad? Thanks good info guys finding very helpful

It really really depends what your goals are and what type ammo you are loading.

For long distance "match" ammo mid range single digits would be desirable, i.e. 5 to 8 or so FPS. For .223 Rem. 55 grain ball plinking ammo there is not much wrong with a SD 25 to 35 (would match some factory ammo I have tested). Match and plinking pistol ammo can stand to have SD numbers a fair amount higher than rifle ammo due to the distances involved. JMHO.

 

[Twoboxer]

This is pretty much the method I was taught, however I was told to subtract 1 from the sum of the squares of the difference off of the mean before dividing by the number of shots and then finding the square root of that number. . . .

I believe if you have the whole population, you do not subtract one. If you have a sample, you subtract one from the number of (in this case) shots.

I found this page simplistic but useful - Standard Deviation and Variance