Standard Deviation

[dhansen]

SD does this sound correct. I shot 20 rounds over my chronograph low=1186 fps & high=1320 fps the mean was 1256.45 fps. I took each of the twenty readings and subtracted the mean, then squared those numbers. Added the twenty numbers together and divided by twenty (number of rounds). Which was 31.505 then the square root of that number which was 5.6. So is my SD 5.6? This is a 44-40 I am working with and using A2400 15gr. with 1.0 cc PSB (polyethylene shot buffer) and a .430" Dia. RNFP lead bullet.

David

[Sweetwater]

The short answer is I don't think so, though I have to get to work and don't have time to explain it all out right now. I'm sure someone will chime in here with the details.

My calculator does it for me and I don't give it a whole lot of thought. My first thought is - an extreme spread of 134fps is too much for my liking and will yield an SD of something like 65fps or so.

Jeff
NRA Life

[Halwg]

The standard deviation is the square root of the variance, which is the mean of the squares minus the square of the mean.

Consider a population consisting of the following eight values:
These eight data points have the mean (average) of 5:
To calculate the population standard deviation, first compute the difference of each data point from the mean, and square the result of each:
Next compute the average of these values, and take the square root:


So I don't think your calculation was entirely correct, unless this was the way you did it.

My other thought is to just plug the numbers into Excel and let the program calculate the SD for you.

[Tatersoup]

I THINK you should have divided the last number by 19, NOT 20, before you took the square root.

An example:

your list of numbers: 1, 3, 4, 6, 9, 19
mean: (1+3+4+6+9+19) / 6 = 42 / 6 = 7
list of deviations: -6, -4, -3, -1, 2, 12
squares of deviations: 36, 16, 9, 1, 4, 144

sum of deviations: 36+16+9+1+4+144 = 210
divided by one less than the number of items in the list: 210 / 5 = 42
square root of this number: square root (42) = about 6.48

[dhansen]

Thanks everyone, Tatersoup on the second from the last step when you divided 210 by 5 that is not what I did. I would have taken the 210 and divided by 6. So this may be what I was doing wrong. Halwg I will look into the Excel thing.

David

[DWB]

Statistics was never an easy subject for me in school. Fortunately, Excel spreadhseets (as Halwg mentioned) are a great way to overcome my intellectual weakness... Better yet, my Pact1 chrono does it all for me... I still maintain records of each individual shot and when I double back on my data and duplicate a test load, I can combine the information from both test lots of the same load on an Excel spreadsheet to update the Avg, ES, SD, and AD.

[dhansen]

DWB, What is AD? Did the math again using the formula Halwg has in his post. Again came up with SD of 5.6.

David

[DWB]

DWB, What is AD? Did the math again using the formula Halwg has in his post. Again came up with SD of 5.6.

David

AD is the average absolute deviation, or average deviation and is a summary of statistical dispersion or variability. In other words, if you look at the average velocity of your load work, the average absolute deviation will tell you, on average, how many feet per second (plus or minus) you can plan on your loads being to the actual average velocity... This number really only comes into play if you have really radical data (with a large extreme spread).

As opposed to standard deviation, which is probably a more useful indication of variance if the individual readings are pretty consistent relative to each other (i.e. a lower extreme spread)

One isn't really any better than the other, except with those examples - - depending on how broad your extreme spread in velocity readings might be... for general purposes, the Standard Deviation is more commonly accepted as an indication of how consistent your loads are.

In either case, the lowest possible SD or AD would suggest a more consistent load. And... Statistics aside... Sometimes, the most statistically consistent loads are the most accurate loads - - go figure - - but sometimes they aren't, and a "statistically challenged" load will produce better accuracy overall... At times like those, the average velocity of a particular bullet, in a particular barrel just produce the proper harmonics - regardless of fine point of the statistics of the particular load.

[swany]

To those who do not know me I am a math guy from my first math class on I have been gifted so to speak. My last job involved working in a Metrology Lab for GM.

Now to the math, it don't mean squat. What means something is working your load until you shoot em all in one spot for the smallest group you are capable of.

Now math means something. It is at this point you get out your chrony and calculate your SD and calculate your trajectory not before you get a good group.

This is the reason I don't believe most folks should have a chrony at every range session, especially if you do nothing but go after speed. 1302fps from a 44-40 using a cast RNFP bullet? Why? I could understand this if using a Gas checked bullet and working for a good hunting load. That bullet and 2400 I would not, try say Unique and shoot for groups then go for the chrony. If it's a plain base start at around a book load of 1000fps if you don't obtain a good load by the time you reach 1200 try another powder.

[capt greg]

those dang guzentas get me evertime....