I have never chronographed a single round I've reloading/fired. Bought one a year or so back and (so far) have never used it. Might be neat, might use it someday when I have lots of time and no one is around on the range (probably need to take it home one weekend and get it figured out on the "range up above the garden".
Over the years I've read of a few instances where a large number for SD still shot very good groups and the person posting about it was curious how they could get such good groups with a large SD. The answer was usually that sometimes that just happens.
Standard Deviation is one measure of consistency of whatever parameter you're measuring/recording. Velocity. No one does it for group size, but it could be done. I don't think anyone does it for cartridge overall length, but it could be.
When I was working as a process/production engineer in one of the plastics industries we would start off with no less than 100 samples (readings of the operational temperatures/pressures/percent power/rpm/percent load, etc., etc., etc. and average all of them together (for that particular parameter). Then we'd let the computer do the calculations to give us the average, the standard deviation and an upper/lower limit of three standard deviations from the average. That gave us the average (say pressure at a point in the process), the standard deviation and +/- 3 standard deviations from that average to use as an upper limit (+3 sd) and a lower limit (- 3 SD).
Then we'd continue to monitor the process (still collecting data from all those places/conditions in the process). We looked for two things.
One was a deviation that was above the upper limit or below the lower limit. If we saw that it indicated a change in the process that could affect the quality of the product or the ability of the process to continue running/making product. The second thing we looked for was 5 or more readings that trended up, or down. That was an early indicator of a slower, but meaningful change in the process that could affect quality, or the process itself. As long as the data points continued to move up/down within that range of upper/lower limits and did not trend up/down more than 5 data points then the process was "normal" and no actions/worries.
That's a sort of short explanation of how we used those numbers/calculations for work. If you see an actionable deviation then you need to do some trouble shooting to find out what has changed in your process.
If you checked velocity on every round you fired you'd look for similar stuff - a change in velocity outside those control limits or a trend up/down. It might mean a change in seating depth, change in case mouth crimp, change in amount of powder, change in case volume, change in bullet weight, etc. Or course, if you check all that stuff at the time you "make" the round you greatly reduce the issues due to things you can control and then you have to look at stuff like primers and powder quality/consistentcy - if you have the resourses/ability to do that.
I just worry about group size. Which, most of the time in my experience, comes with loads somewhat less than maximum pressure/velocity.
An illustration of different numbers that give similar results for average velocity , except for standard deviation. Which one would you rather have for your new load?
vel/fps vel/fps
1500.00 1250.00
1400.00 1270.00
1300.00 1240.00
1100.00 1260.00
1000.00 1280.00
1260.00 average 1260.00
207.36 sd 15.81