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Is there an easy way to compute SD from your extreme spread?

Don't think that's the way to do it.

Find a SD calculator online. Probably will ask you to type in your velocities. It will calculate SD from them.

Unless you are trying to find the standard deviation of multiple "extreme spread" numbers from a bunch of different range sessions with one load.

Maybe mathman will be along to help

Manage ES and SD becomes irrelevant.





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It's all pointless unless you figure in BC as well.

Sure don't understand this comment. What does BC have to do with ES and SD? Do you mean unless you consider BC (and of course, velocity too) you can't know the effect of SD and ES downrange?

Seem the answer to reo's question is the same whether BC is .200 or .600.
And the answer is, "no."
You can't figure out SD from ES because the size of your sample (the number and value of the different velocity readings you have between the low and the high that make your ES, matters, even if the average velocity and ES are the same. For example, consider the following samples of velocities, all of which have the same ES and the same average velocity (50 and 3025):
a) 3000, 3050. Average = 3025, SD = 25
b) 3000, 3025, 3050. Average = 3025, SD = 20.4
c) 3000, 3010, 3020, 3030, 3040, 3050. Average = 3025, SD = 17
d) 3000, 3025, 3025, 3025, 3025, 3050. Average = 3025, SD = 14.4
I just use online tools any time I need to calculate SD (usually when I forget to hit Reset on my Oehler between groups.)

Hope this helps,
Rex

Yes, there is an easy conversion. I will post the numbers when I get back to my home computer.

Golly gee, I wonder if the winking emoticon could imply anything...

It was meant in jest as I am one of the dinosaurs who gets lost in the world of such things. I was going to include rpm, mpg, and gnp to emphasis that, but I just went with the wink.

It doesn't matter.
I use an Oehler 35P and measure every shot I ever fire at a range which calculates those numbers at the push of a button and you can control how may shots are in the sequence but what really does matter is the consistency of multiple groups.

I have seen extreme spreads of over 200fps that shot beautiful tight groups just as well as groups with single digit deviation. If I drew conclusion from the readings and ignored the good groups I would be falsely reporting the results. So, while the theory is sound and the maths can substantiate the theory, a good group is a good group and a best load is the average of s series of groups shot under similar conditions.

Every single reader gets interested when they see a nice round tight group on paper. Every single ready has had a good day a the range and shot just such a group. None of this matters unless you can shoot with more consistency, so that the load generates repeatable grouping which proves that consistency. That is why you see single grouping on targets more often that not. The guys who posts a target sheet with a half dozen groups with the natural spread we all get are the most valuable communicators. That is the proof od the load and the consistency so if they are all similar, round or touching and under MOA at your preferred range, you have a good rifle and load and you shot well. The Extreme Spread and Standard deviation is less informative that the final average grouping over the single groups and ES+SD readings.

Now after that, I have seen more velocity spread with faster powders in larger cases that with slower powders in larger cases, especially with smaller bores. ES and SD, yes I note it, Yes, I record it, but the groups is the arbiter of the load and the consistency of repeat grouping is both the educator and the sum of all.

A way to calculate SD just from Extreme Spread? Anxious to see this.
Thanks,
Rex

Oops, Sorry, it's been a long day and I missed the joke. Hope my reply was not taken as offensive, certainly not meant to be.

Cheers,
Rex

Standard deviation is a measure of dispersion, how spread out the data are. So also is range (what shooters call ES). So there has to be a conversion between the two. It is known as the d2 (d subscript 2) constant.

As you get more items in a sample, range will tend to grow, because adding a point to the data never makes the range smaller, and sometimes makes it larger. So the conversion factor depends on the number of items, n.

For n=2, d2=1.128

n=3, d2= 1.693

n=4, d2= 2.059

n=5, d2=2.326

n=6, d2=2.534

n=7, d2=2.704

n=8, d2=2.847

n=9, d2=2.970

n=10, d2=3.078

To get standard deviation, divide range by d2.

For small n, standard deviation will tend to underestimate actual long term dispersion. Range doesn't do that.

The standard deviation you get this way won't generally exactly match what you get from the calculator. That is because there is so much uncertainty in estimates of variation based on small samples.

All excellent points. Like you, I also use the 35P for almost every round I send downrange from the bench, and I have certainly seen the same - tight groups (at 100 yards) that had big ES, and big groups with single digit SD. I fear the tight groups with big ES would not open up in a linear manner as range increases (assuming no wind), as a tight group with a low ES would tend to, though, but rather increase in size at a greater rate than range increases.
But I do have to disagree with the opening sentence, "It doesn't matter."
It matters to the OP, because he is looking for input on a question of fact - "Is there an easy way to compute SD from your extreme spread?" IMO, this question makes no value judgement on the applicability or usefulness of velocity numbers, it's just a question about math.
I think the answer is "no" and tried to provide examples to illustrate, but Mr. denton says there is an easy way and I am happy to listen and consider his response.

Cheers to all,
Rex

Not a problem at all.

WARNING: Total geekery follows (perhaps encouraging the earlier point - "It doesn't matter" ;o))

Thanks denton, this makes more sense - you can't approximate SD from ES (range) alone, but if you know "n" you can. I applied the d2 values above to my examples and got reasonable agreement when n was large (6) but far off when n was 2 or 3. In going back to re-run my numbers I used a bunch of different online calculators and in the process ran into something new to me, the difference between "population SD" and "sample SD". Looking up the difference I found this:
"Population standard deviation is the exact parameter value used to measure the dispersion from the center, whereas the sample standard deviation is an unbiased estimator for it. • Population standard deviation is calculated when all the data regarding each individual of the population is known."

So I figured when we calculate SD for a string of measured velocity readings we ought to use "population SD" (which, only by accident, is what I put in my examples). It looks like the d2 method provides a closer approximation to sample SD than population SD, but it's always greater than either in this limited sample.

Going back to my examples and adding sample SD (from online calculators) and d2 SD estimate shows:
a) 3000, 3050. Average = 3025, population SD = 25, sample SD = 35.3, d2 SD = 44.3
b) 3000, 3025, 3050. Average = 3025, population SD = 20.4, sample SD = 25 , d2 SD = 29.5
c) 3000, 3010, 3020, 3030, 3040, 3050. Average = 3025, population SD = 17, sample SD = 18.7, d2 SD = 19.7
d) 3000, 3025, 3025, 3025, 3025, 3050. Average = 3025, population SD = 14.4, sample SD = 15.8, d2 SD = 19.7

Now this got to wondering which SD the Oehler "gonks." I figured for sure it would use "the exact parameter", or population SD. So I pulled out the saved tape from my last range session and ran a few of the strings through an online tool that outputs both population SD and sample SD, and guess what - the Oehler outputs SAMPLE SD. I don't know why unless the reason is that maybe it is a better predicter of what you might get in the future from the same load?

Learned something new today. But recommend reo just use one of the online tools to calculate his SD, ideally one that outputs both sample and population SD. And if you want the same value the Oehler outputs (must be the "good" one, right) record SAMPLE SD.

Well, that was kind of like fun, but not quite...
Cheers,
Rex

I'm not sure you've grasped population vs. sample SD.

Gotta love statistics discussions.

This.

Population includes all possible shots ever fired with that load and barrel, and is rarely known. Sample includes all the values actually measured in a string.

Well put. The greater the sample size, the more representative of the population. The more shots tested, the more those shots will represent that load in that gun.

Thanks, that is a much clearer explanation than I found online, but does seem almost opposite of the quote I posted above that purported to describe the difference.
Mathman, is that your take on it too. Since your handle is Mathman I will automatically believe anything you say...;o)

Thanks fellas - until today I wasn't even aware of the distinctions.

Rex