We got an interesting question from a reader wanting to know how to compensate for standard deviation of his muzzle velocity. His question points to a broader misunderstanding about descriptive statistics. So, we’d like to help out.
When we talk about averages and standard deviations, we are using statistics to describe a normal sample representative of a population. So, we make inferences about a population through sample analysis. In this case we’ll be talking about ammunition.
As we all know, manufacturing processes are not perfect so you’ll never get a round of ammunition that chronographs at exactly 2600 feet per second even across the same lot. The reasons for that are practical in nature, machine tolerances are not exact, machines loose alignment, it’s simply the way things work. I suppose one could produce ammunition that chronographs consistently at 2600 fps out of the same barrel at the same temperature and across the same lot. But, the reality is that even if it were achievable, you would end up paying 100’s of dollars per round. Not very practical ! So, we use statistics to help us describe a population, in this case the population is all of the rounds that make up the same lot of ammunition. In testing, manufacturers fire many rounds from test barrels and those shots are chronographed to determine average muzzle velocity and standard deviation. If the standard deviation is out of spec, the manufacturer revisits the manufacturing process; making the necessary adjustments to bring standard deviation in spec.
The standard deviation is a mathematical indicator of how tight your distribution is. For example the curves below.
The red curve has a larger standard deviation than the green curve. Because the standard deviation of the red curve is larger, the shooter can expect greater variability from the average muzzle velocity across the lot. The green curve has a smaller standard deviation so the muzzle velocity across the lot will be tighter having less variability.
Plugging some numbers into the discussion, let’s say we chronograph 5 ten shot groups from ammunition produced by a manufacturer that’s all part of the same lot, and our chronograph indicates an average muzzle velocity of 2203 fps with a standard deviation of 17 fps. This means that 68% of the time you fire ammunition from the manufacturer’s same lot, your muzzle velocity, given the same barrel and temperature, will fall between the rage of 2,186 fps. to 2220 fps.
Notice all of the variables involved: manufacturer, lot number, test barrel, your barrel and temperature. So, the long and the short of this is that you don’t compensate for standard deviation it simply lets you know what to expect 68% of the time you shoot with the ammunition. The smaller the standard deviation, the more consistent your muzzle velocity will be, all other things being equal.