As your post implies, the chronograph is a measurement tool. It's purpose is to aid in developing loads to meet a specific goal. One goal may be accuracy throughout a give range of distances, or a specific distance......or to achieve or maintain a minimum momentum.
For the vast majority of us, it also requires a ballistic calculator to assist in forecasting the desired results at longer distances (600/800/1,000 yards), based on the measurement we get at a closer distance (muzzle/100/200 yards).
Extreme spread, gives us an idea how consistent our handloads are. If we use a 10 round sample, the slowest being measured at 2,800 fps and the fastest at 2,825 fps.....our extreme spread would be 25 fps and that would be considered good. If the low was 2,750 and the high 2,820, the extreme spread climbs to 70 fps, not so good, and that would indicate we may have a problem with our loading technique (mixed brands of brass, extreme variation in neck tension, etc.), or perhaps the primers and powder we combined do not favor each other.
A large extreme spread is seldom good, but a smaller extreme spread is just part of the reading and may not indicate an accuracy load.
The average muzzle velocity can be used effectively to forecast momentum and at what distance the bullet will fall out of supersonic flight, but does not provide a lot of information for accuracy.
Standard deviation is a key measurement for accuracy. Uniformity of velocity is key to accuracy and standard deviation is a statistical measurement of uniformity. It is also the least understood and the more difficult to calculate (by hand anyway). It's the spread of difference within about 2/3 thirds of the sample. A standard deviation of 8 fps would be very good, as opposed to 20 fps which would be fine for many uses, but probably not for accuracy loads. The 2/3 of the sample are the 2/3 which are closest as to being the same.
Using the standard deviation as a reliable measurement requires a reasonable size sample. A statistician would like as large a sample as possible, often outside of reason. Probably the most recognized sample as useful would be 20 rounds. That doesn't have to be a 20 round group, it could be two 10's, four 5's, or any combination, as long as the sample was collected at the same time, or within reasonably same conditions (same temperature, humidity, altitude, pressure, same lot of components.....some of which has little effect, but you get the idea).
If we can get at least 2/3 of our handload to measure a very close to the same velocity, it implies the combination or case, primer, powder (and how much), bullet, seat tension, seat depth, bullet runout, and loading technique.....should.....be an accurate load, for at least some distances.
If we launch bullets at the same velocity, they should have the same trajectory. At a given point in the flight path of the bullets, they should all group close together. If one bullet is slower and/or faster than others, the trajectory is going to be different in comparison, and it goes to reason, the bullets will impact higher, and/or lower, than others.....opening up the group.
In application, we will never get all the bullets 9some maybe, but not all) to launch at precisely the same velocity, but we know the closer we come to the same, the more accurate and uniform the loads should be. For me, I strive for 6 fps standard deviation, with a maximum extreme spread of 18 fps. I don't always get it! But, I always attempt to reach that goal.
For a quick and dirty initial reading (usually in the field without a standard deviation calculator), we would chronograph 10 rounds, subtract the high reading, subtract the low reading, and average the remaining 8 readings. This method doesn't replace a standard deviation calculation, it just gives us a quick "look see" indicator. Fortunately, most chronographs provide standard deviation calculations for a specific string (sample).
So, a small standard deviation, combined with a small extreme spread, which obtains the minimum average velocity......should give us an accuracy load! In practice it accounts for one of the puzzle pieces......it's important, but may not solve, or provide, the accuracy we seek.
Not withstanding the breech, firing pin, chamber, throat, twist, barrel length, and rifling.......what at the loading bench effects standard deviation at the chronograph? Just about everything we touch and do! From the selection of component combinations, to our technique of preparing the brass and putting it all together. One thing which effect all the other specifics is.....consistency. We strive to use better techniques and better tools, but using those tools consistently, just like in our shooting skills, is a key component to success on target.
.......well not everything I have said is absolutely 100% correct, but for saving time and space, taking one step at a time, I think it is pretty close to being accurate!
Best Regards.......Eagle Six