Could someone explain standard deviation as it applies to reloading?

It's a statistical (mathamatical) number that describes the probable range of observations from a sample.

If one takes the standard deviation and multiplies it by 6.2 he (theoretically) will have the extreme range of 99.9% of all the observations he will ever see.

Example:.....you're shooting over a chrony and it gives you a standard deviation of 23.

You then know that the extreme velocity spread of that load is 140'/sec. Obviously small SDs are best but it's not a number to get too excitd about. It's just one number in a sea of numbers.

Look at your groups and screw the SD!!!!!

Standard deviation a measure of the amount that one velocity you measure will vary from the average velocity.

If you draw a picture of the standard deviation of velocity it looks like a bell shape curve. The majority of the measured velocities will be within one standard devaition of the average.
If the average velocity is 3000 fps with a standard deviation of 50 fps, then approximataly 66% (one standard deviation) of the shot that you take will be between 2950 and 3050.

Two standard devaitions is around 90% (it's been too long since I took statistics). 90% of your velocities from the previous example would fall between 2900 (50 fps * 2 std dev. - the average) and 3100 (50 fps * 2 std dev. + the average).

Three standard devaitions is 99.9%. 99.9% of your velocities from the previous example would fall between 2850 (50 fps * 3 std dev. - the average) and 3100 (50 fps * 3 std dev. + the average). As previsouly stated if you take six times the SD you get the extreme spread or maximum difference between the lowest and highest velocity you should see in your ammo.

Ammo with a low SD will have more consistent velocity and is usually, but not always more accurate. It is only one factor. It's nice to know that you have consistent velocity, but actual group size on the target is what counts.

quote:

Originally posted by vapodog:

If one takes the standard deviation and multiplies it by 6.2 he (theoretically) will have the extreme range of 99.9% of all the observations he will ever see.

Example:.....you're shooting over a chrony and it gives you a standard deviation of 23.

You then know that the extreme velocity spread of that load is 140'/sec. Obviously small SDs are best but it's not a number to get too excitd about. It's just one number in a sea of numbers.

Vapo: Where in the world did you get that one? From a traveling math salesman?

An SD of 23 on a two-shot string would represent an extreme spread of 46 fps. On longer strings, the extreme spread would likely increase with an SD of 23, but to say that it averages "6.2x the SD" is off the wall. Again, where did that come from?

quote:

Vapo: Where in the world did you get that one? From a traveling math salesman?

An SD of 23 on a two-shot string would represent an extreme spread of 46 fps. On longer strings, the extreme spread would likely increase with an SD of 23, but to say that it averages "6.2x the SD" is off the wall. Again, where did that come from?

Take a class in statistics.....it's a mathamatical proof and absolutely true.

Further it's consistant with the explanation that elkhunter has posted...as follows:

quote:

As previsouly stated if you take six times the SD you get the extreme spread or maximum difference between the lowest and highest velocity you should see in your ammo.

It's actually 6.2 but who is counting small stuff?



If anything is off the wall it's this statement:

quote:

An SD of 23 on a two-shot string would represent an extreme spread of 46 fps

Look back and see who made that one!!!!!

quote:

Vapo: Where in the world did you get that one? From a traveling math salesman?

Actually it comes from the University of Wisconsin......

hvy

It seems that this question comes up every couple of days on this and other shooting forums and it very quickly gets bogged down to where the original poster gives up and goes back to watching TV. Math can be confusing and what seems like a simple answer to some may be incomprehensable to another. Let me try:

Standard Deviation measures how spread out the values in a data set are. It measures the average distance of the data values from their mean. If the data points are all close to the mean, the SD will be low. If many data points are different from the mean the SD is high.

An example. You chronograph 5 shots.

3250
3247
3206
3256
3250

The average is 3242 and the extreme spread is 50. The SD will be low.

Five more shots:

3256
3240
3229
3206
3230

Average is 3232 but extreme spread is still 50. SD will be high.

The better load? Probably the first one. (Only actual shooting will tell for sure.

Ray

quote:

Originally posted by elkhunter:
Standard deviation a measure of the amount that one velocity you measure will vary from the average velocity.

If you draw a picture of the standard deviation of velocity it looks like a bell shape curve. The majority of the measured velocities will be within one standard devaition of the average.
If the average velocity is 3000 fps with a standard deviation of 50 fps, then approximataly 66% (one standard deviation) of the shot that you take will be between 2950 and 3050.

Two standard devaitions is around 90% (it's been too long since I took statistics). 90% of your velocities from the previous example would fall between 2900 (50 fps * 2 std dev. - the average) and 3100 (50 fps * 2 std dev. + the average).

Three standard devaitions is 99.9%. 99.9% of your velocities from the previous example would fall between 2850 (50 fps * 3 std dev. - the average) and 3100 (50 fps * 3 std dev. + the average). As previsouly stated if you take six times the SD you get the extreme spread or maximum difference between the lowest and highest velocity you should see in your ammo.

Ammo with a low SD will have more consistent velocity and is usually, but not always more accurate. It is only one factor. It's nice to know that you have consistent velocity, but actual group size on the target is what counts.

This is actually a very good explanation...better than mine I might add.

Stonecreek.....are you paying attention?

Does anyone have an easy way to calculate standard deviation?

woods

If you Google "standard deviation" you can find several. Also, I think there may be pocket calculators that have a function built in. I couldn't tell you if one is easier than another since I am math-ignorant and wouldn't know an easy one if it bit me in the a$$.

Ray

quote:

Originally posted by Cheechako:
woods
I think there may be pocket calculators that have a function built in.
Ray

Texas instruments has several but the best is one called statistical calculator.....or business analyst II

Many others do it.

In fact the standard deviation helps to understand a bit but you'll live just fine without it. IMO it's not a critical number at all.

The formula is somewhat complicated and there's two formulas....one for normal stuff and another one for observations of less than nine.....

One divides by "n" and the other by "n-1"

Really.....you're not missing much at all.

quote:

Originally posted by Cheechako:
...I think there may be pocket calculators that have a function built in. ...

Hey Ray, Right in the old 10X.

Hey Woods, You can pick up a Scientific Calculator for as little as $10 which will lead you right through the Data Entry and toss it right out for you.

My "first" TI Calculator was $150 way back when they were "Water Wheel Powered" and today you can get 100x the power and capabilities for 10% of that.

You can even get one that does a visual Graph of the shots(Data Points), the Bell Curve and all the things mentioned above for $25-$35.

Then once you know the SD, n-1 weighting the graph and all, check the """Target""" to see which Load is the best.

quote:

Originally posted by vapodog: IMO it's not a critical number at all...Really.....you're not missing much at all.

I agree! When I do my chronographing if the SD and AD are little numbers I smile. If they are big numbers but the bullets all go into a tiny hole I smile a lot.

Ray

If you are running Windows on your computer, it has a calculator that will do standard deviations.
Click on "Start", then "Programs", then "Accessories", then "Calculator"; this will start the calculator program.
Open the "View" menu, and select "Scientific"; this will add all the extra buttons needed to do statistics.
Click on the "Help" menu, and click on the "Help Topics"; which will open a help window, then Click on the "Contents" tab if it isn't already displayed.
Click on "perform a statistical calculation entry" for directions on how to enter your raw data.
After the raw data is entered (and you have clicked on the "Sta" button, just click on the "Ave" button for the avereage of the entered data, and click on the "s" button for the standard deviation of the entered data.
For Cheechako's first set of data, the average is 3241.8, and the standard deviation is 20.27 For the second set of data the average is 3232.2 and the standard deviation is 18.23

quote:

Originally posted by CMcDermott:
If you are running Windows on your computer, it has a calculator that will do standard deviations.
Click on "Start", then "Programs", then "Accessories", then "Calculator"; this will start the calculator program.
Open the "View" menu, and select "Scientific"; this will add all the extra buttons needed to do statistics...

Well...., DUUuuuuuuhhhhh on me.

Thank you Mr. McDermott!

I use the Windows Calculator ALL THE TIME and never even noticed the Scientific MODE being available.
---

NOTE TO myself: LOOK at the Options when using the computer!!!

HC

You have a computer??!! I thought you dictated these posts to your grandkids and had them put them on the web!!

PS - bet you have an old computer.

Thanks for that info McDermott. I did a search on standard deviation and even though I minored in math in college, I couldn't figure it out.

quote:

Originally posted by woods:
...PS - bet you have an old computer...

Hey Woods, I think it is an original "Abacus" model.

Let's see here, something about "AMD 64 Athlon" Processor in it. Had to replace the "older" one last year.

Even had one with an "8088" Processor in it at one time. That was back when a lot of folks figured "Windows" was a Flash-in-the-Pan Program.

He who lives by the Hard Drive - Dies by the hard Drive.

Here is how I use standard deviation when testing loads & loading techniques.

1) Even if I shoot only 5-shot or 3-shot groups, I will use at least 9 shots to calculate the SD. For example, if I shoot three 3-shot groups, then I use all 9 shots to calculate standard deviation. Or if I shoot three 5-shot groups, then I use all 15 shots to calculate SD. This is important. You cannot calculate a meaningful SD with only 3 shots or 5 shots, even though gunwriters and chronographs do it all the time.

2) I do see a correlation between accuracy and standard deviation. The correlation is at best weak, and sometimes it's not there at all, but over the course of testing hundreds of loads, there is a correlation more often than not.

3) I especially value SD for testing primers and crimps. Primers and crimps directly affect ingition which in turn affects SD. You want to know which primer is better with your load ??? Simple -- compare SDs for at least 10 shots with each primer. I also value SD for testing cast bullet lubes, since the bullet lube affects bore condition and gas sealing and both affect velocity. I don't use SD so much for comparing bullets.

4) I record each shot's velocity at the range and later use a spreadsheet to do the calculations.

5) While accuracy is more important than SD, accuracy is subject to human error and range conditions, especially in lightweight firearms. As with all data comparisons, it takes a lot of group shooting to prove anything. One group doesn't prove anything. Even three groups doesn't prove much, statistally speaking. Generally you will need at least 5 groups to prove a statistically significant difference in accuracy, and even 5 groups is skating on thin ice, unless the accuracy difference is dramatic. Chronographs, on the other hand, are pretty reliable as long as the light conditions are decent, and 10 shots will usually suffice to prove a stastically significant difference in velocity or SD. We are talking about needing only 10 shots to prove something with a chronograph vs. 50 shots to prove something by group shooting. That's a powerful tool. Use it wisely and enjoy.

Let's take a step back here, and try and get a feel for what SD really describes. The definitions given are good, but maybe this will help to visualize it.

Imagine a bell curve. It has two dimensions: height, and width. The Extreme Spread is the width of the curve. SD describes how HIGH the curve is. The higher the peak of the curve, the more of the observations are right around the mean, the smaller the standard deviation. A very flat bell curve can have the same extreme spread (same width), but a very low peak. That would be a curve with a higher standard deviation.

So, SD is a mathematical representation of how tight the observations are around the average. HTH, Dutch.

quote:

So, SD is a mathematical representation of how tight the observations are around the average. HTH, Dutch.

Now that's an excellent statement....as good as it gets.....at least for those that have not taken the full blown classes in Mathematics.....excellent post.

Thanks guys, I appreciate the responses. I think that I see how I can use the Standard Deviation now.

Most spreadsheets will also have average and SD functions.