The M193 represents the old military system, in use for about a century:

Shoot a group of 10 shots and measure the coordinates of each impact.

From this, calculate the mean point of impact (MPI).

From the MPI, measure the radial distance of each of the shots.

Take the sum of the radii and divide by 10: this is the mean radius.

In typical acceptance tests, 9 shot groups were used and the average mean radius taken. In special cases, 180 shots (18 groups) were used. From a statistical point of view, mean radius is an excellent measure of dispersion, its quality comparable to standard deviation.

Adoption of M855 and M856 brought the change to compute the standard deviation in place of mean radius. It is computed for vertical and horizontal dispersion separately. At the same time, the procedure was changes from 9 groups of 10 shots to 3 groups of 30 shots. So the total of 90 shots was kept.

“Standard deviation”, a little complicated to describe, is used in engineering worldwide. You can look it up in any textbook or ask an engineer or a math teacher.

I would not be surprised if Dvoryaninov describes the above process in detail.

For the Western readers: In Russia, 20 shots are fired and the mean point of impact determined as above. Then the radial distance of each shot is measured as above.

Counting from inside out, the radii of the 10th and 11th impact are added and divided by 2. This is called R50 and used as the acceptance criterion. 3 groups are fired, meaning 60 shots.

This R50 figure can often be found on ammunition flyers from former Eastern Bloc manufacturers.

Caveat: The above is based on publicly available documents. Changes may have taken place.