From Chrony:
“
Standard Deviation, population, (-Sd-)
Multiply the square of the average velocity by the number of shots and deduct it from the sum of the squares of all shot velocities, then divide this total by the number of shots minus 1, and then take the square root of this figure.
For example: [(29902 + 30102 +29962 + 30042 - 4 x 30002) ÷ (4-1)]½= 9 FPS
Standard Deviation is a measure of how close each shot’s velocity will be to the "average" shot. It is called STANDARD because it is computed in such a way that it has a standard meaning when compared to the NORMAL CURVE. Nearly all things we measure fit a normal curve [such as the height of people, the diameter of (supposedly) identical motor pistons, and the velocity of (supposedly) identical cartridges]. The NORMAL CURVE shows that all variables occur more frequently at or near the average, and less frequently as they deviate further from the average. We use a STANDARD Deviation measure so that all things we measure can be compared with each other and to this curve [68% of all things we measure falls between one standard deviation above or below average, 95.4% falls between two Standard Deviations above and below the average, and 99.7% falls between three Standard Deviations above and below the average]. Thus, Standard Deviation is a universal method in statistics and measurement for dealing with and interpreting data.
Therefore, if the bullets are traveling at an average velocity of 3000 feet per second, and there is a Standard Deviation of 20, then 68% of the shots you fire will fall between 2980 and 3020 fps, and 95.4% will fall between 2960 and 3040 fps. Nearly all of them (99.7%) will fall between 2940 and 3060 fps.
Since Standard Deviation is the most important information your chronograph can give you, it is useful to understand the reason for this. At least ten (10) shots are required to obtain a reliable average and Standard Deviation. Fewer shots (such as 3 or 5) are typically "small samples", and are considered unreliable when measuring anything variable.”