Your extreme spread is 93.
Standard deviation is quite a complicated statistical formula.
- first you find the average velocity (2923, as you said)
- Then, you find how much each shot deviates from the average (ex. your high shot deviates from the average by 50 fps, the lowest by 43; you need to find the deviation for the other 13 shots as well
- Third, square all the deviations and add them together.
- Fourth, divide by the number of samples (in this case, 15)
-Finally, find the square root.
I was shooting a variety of loads this past weekend, SD ranged from 40 down to about eight. I was sharing some of the data with the guy at the bench next to me and he commented that he considered any standard Deviation under ten to be a very good number.
Nice, clear explanation of SD. There is nothing magical about standard deviation and what it means, when you are using it as a descriptive statistic, either. The bigger the standard deviation, then the more variable the scores, in this case velocities, you are measuring. One reason the SD is used is because it has a certain relationship to the mean (average). In other words, it cuts off set amounts of scores around the mean. As an example, unless things have changed, the average IQ is 100 and the standard deviation of IQ's is 15. So, just over 68% of IQ's lay between 85 and 115 (plus or minus 1 SD around the mean) and just over 95% between 70 and 130 (plus or minus 2 SD's around the mean).
When looking at loads for shooting I generally just use the range (biggest minus smallest).
The main potential problem with using the range is that it is very easily affected by one or two unusual scores. But most guys would notice this, and think about it, if it happened with velocities they were measuring. As to how large the range should be; smaller is better, obviously. Smaller means less spread in the shots due to velocity differences. I am unaware of any simple rule beyond this that tells you what an acceptable range is. (You could choose a standard. One might be what factory ammo gives you. Another, the one I tend to use, is how low the range is in my friend's reloads.
) As far as I can see, having a low range or spread in velocities seems to matter the further out you shoot and, in my experience, shooting at 100 meters doesn't tend to tell you much about this. One of the best groups I have shot with cast bullets at 100 meters with my hunting rifle, for example, was 1 1/4 inches (5 shots) and it had a velocity spread (range) of 180 ft/sec (just happened to be chronographing at the time). I'm sure the group would be all over the place in vertical spread by about 200 or 300 meters. Most loads used by precision shooters who are shooting long range probably have very low ranges in the velocities yielded by their reloads. Don't know about the big boomers, but I doubt in the smaller target rifles the ranges would be larger than 30 ft/sec and probably much smaller.
The standard deviation by the way will always give you a smaller number than the range. Could be one of its attractions
. As an example, the following scores; 1,2,3,4,5 have a range of 4 (or 5 depending on how you calculate it) and a standard deviation of 1.4...
Please excuse the run on, probably more than you ever wanted to hear about statistics.
respectfully, fred
