I understand Extreme Spread. Now what is the difference between Extreme Spread and Standard Deviation? I would like to know how an Extreme Spread of 50fps can equate to a Standard Deviation of 16fps. Not trying to be smart just am now at the point in my shooting where I need to get familiar with all this. Good thread.
Standard Deviation is a better statistical measure of how a series of numbers varies. Tthat wikipedia page has the math of it, but it probably isn't terribly interesting or useful. The takeaway is, "SD is a better measure of the variability of a shot string, but ES is easier to calculate"
As a practical matter, for most real-life samples of muzzle velocities, it will usually be the case that the SD of the string is about one-third the ES of that string. The attraction of ES is that it's easy to calculate (find the difference between the fastest and slowest shot in the string).
Here is a list of 10 random numbers (normally distributed, for the statisticians in the room....) that I just generated on my computer: {2900., 2906., 2893., 2903., 2895., 2907., 2884., 2891., 2942., 2898.} Consider these to be (simulated) chrono readings.
The StandardDeviation of that sequence is 15.7
The slowest shot is 2884 and the fastest is 2942, so the Extreme Spread is 58.
The ES is "about 3X" the SD (Actually in this particular case, 58 is 3.7X bigger than 15.7, which is a bit of an outlier to my "about 3X" guideline but I am going to leave it in as an example of real life "noise" that is part and parcel of actual statistical samples. In subsequent "tries" I got results of 2.92X, 3.02X, 3.24X, 2.64X etc.... ). That's another, VERY IMPORTANT stats lessons - things fluctuate!
I have (cheapy) chronograph that reports mean speed, and both SD and ES. I write all three down in my ammo log book - the above I would record as "2902/58/15.7", which means an average speed of 2902fps, an ES of 58fps and an SD of 15.7. This is ammo that I would be willing to shoot at 1000yards if I didn't have any better ammo on hand, but it is a bit sloppy; call it the bottom end of "acceptable-but-not-great 1000 yard ammo". I would absolutely shoot it in competition at 600 yards without hesitation, even at a national championship.