In using the "Point Blank" ballistics program, one input that is asked for is standard deviation. Is this term relating to differences in velocity of the round? Specifically I'm plotting the trjectory of the Winchester USA Brand 45gr HP (white box)for the .223 with a muzzle velocity of 3600fps. How crucial is this input? Thanks

It is a statistical term designed to cause confusion.

Here are a few links to the definitions of standard deviation
Standard deviation1

Standard deviation2


Here is a calculator of standard deviation Standard deviation calculator

Standard deviation is simply a means of determining the usefulness of your information.

Using the calculator you can come up with these results:

If you shoot 3 shots of 3290, 3300, 3310 fps the mean is 3300 FPS the standard deviation is 8.1

If you shoot 3 shots of 3000, 3300 and 3600 the mean is 3300 fps the standard deviation is 244

The smaller the number the better.

I am not familiar with your particular program, but I can give you some help with standard deviation.

Standard deviation is just a special type of "average deviation". It measures how spread out your data are. The higher the standard deviation, the more spread out your data are.

For small groups, say three, or five, range (maximum spread) is practically as good, and is simply the largest number minus the smallest.

Hope this helps.

Is there a simple explanation of why root mean square is a less useful tool than standard deviation?I know RMS has been used to describe surface finish, and seems that it would be less troublesome to compute. I know that any modern calculator does this instantly, but I've always suspected it was used to flummox the untutored.
Cheers from Darkest California,
Ross

Ross, I've been doing stats pretty intensely for the past six years. I have often puzzled about the same thing. None of the other stats professionals that I know knew the answer either!

Finally, I had the ear of Don Wheeler, who is one of the 3-4 top statisticians in the world, and I asked him. The answer kind of tickled me.

Before 1925, the stats world used root mean square deviation rather than standard deviation. In 1925, Fischer came out with his book on ANOVA, which had a very profound influence on stats. In order to get his math to work, he divided by n-1, which gives standard deviation, instead of n, which gives root mean square deviation. So, as a matter of convenience, the world went to standard deviation, because the math matches one of the most powerful stat models ever devised.

There is no difference in the information content of standard deviation, and root mean square deviation. You can use either, equally well. It is simply a matter of convenience to use SD.

Generally, RMSE would be used in PCA or PLS analysis of a problem, it is a way to account for the changes a variable has on a given component of a data set.
Example: You make raspberry jam for a living. You want o know
1. When is the best time to pick the raspberries? Early, middle, or late in the season.
2. Which of the four farms you buy from grow the best fruits.
3. Your focus group has decided there are 5 different traits to jam that make it "jam".
Taste, color, sweetness, crunchiness and smell.
Using a professional level statistical program such as The Unscrambler, you can use all those variables and determine where your outliers are, what weights each of the components given, which ones are the most important, having the greatest effect on "jam". The RSEP would be useful in determining your ability to detect which particular components are the most important, so you can focus on them. Here is a mor detailed description.
http://en.wikipedia.org/wiki/Root_mean_square

Standard deviation by comparison is trivial.

For those of us not inclined to obsess about things other than what relationship the holes in the target have to each other, SD is a number.
Lower is usually better than higher, but the target may actually not show this if the higher number is not very high.

Do not be deluded into thinking that a load with a low SD will be a better shooter than a load with a slightly higher SD ( I said slightly, not alot ).

I have seen, with my own eyes, loads that shoot better than others. And SD for the better was more than the SD for the others.

In technospeak :
While the correlation of standard deviation to dispersion of the projectiles may assume to be self evident, the dispersion may indeed be somewhat less for a given segment of the studied population than the estimation of standard deviation would normally allow. This seems to be anomolous to the indication of conformity described by the abscence of deviation of the studied population, perhaps due to variables which were not referenced in the instrumentation of the afformentioned experimentation.

So, like watch the target dude.
Cuz honestly nobody but a hardcore statistics guy would ever go to the trouble of doing this calculation longhand.
And most of us would not even use it if it was not a " one button " operation of our chronos.

The extereme spread of velocity will tell more than the SD ever will about the performance of the load at longer ranges.

Travis F.

Well, since we arlready hip deep in this, why not one more?

Comparing means is fairly easy. Comparing standard deviations is a good deal more difficult. It takes more data, and most of the good tests are VERY sensitive to non-normality.

So if one batch of ammo shoots with an SD of 25 fps, and another shoots with an SD of 15 fps, there is a better than fair chance they are actually the same. It's hard to make the case that they are different, unless you have a lot of data. Variation is a slippery devil.

Nitroman, be careful... your post takes the first steps toward inventing ANOVA. Then we shall have the N test, after Nitroman, rather than the F test after Fischer!!

When you divide by (N-1) then for small sample sizes it will give you a larger number to account for what you don't know from takeing a small sample. So as you increase your N then the (N-1) comes closer to N and your answer should more closely resemble the actual number.

The extreme spread may give you the wrong information if you have one shot that is way off from the others, but the SD will not show as large of an increase with only one shot way out.

It is true that small samples tend to underestimate the standard deviation of the population. The correction for this is the C4 factor.

Standard deviation is defined as the square root of the sum of squares, divided by degrees of freedom, which is ordinarily n-1.

There are all kinds of stat books, and instructors, who have made up their own explanation of the n-1 thing. It frequently gets taught wrong. For example, it is not uncommon for instructors to incorrectly teach that you divide by N if you are calculating the SD of a population.

n-1 is not the correction for underestimating variation. It's just the definition of SD.

Wow, there are some knowledgeable statisticians on this board!

All I know is, a small standard deviation means there's not much variance in the data points. In this case, that's probably the velocities of the rounds you shoot. If the velocity doesn't change much from round to round, the point of impact shouldn't change much.

A larger standard deviation means the velocities from the rounds you fire vary more. Which probably means the points of impact vary more.

If you don't want to go to the hassle of finding a standard deviation, enter a small dummy value, like 1-5. That would assume the velocities among the rounds you fire are very consistent.