Accession Number:



Shot Group Statistics for Small Arms Applications

Descriptive Note:

Technical Report

Corporate Author:

Marine Corps Systems Command Quantico United States

Personal Author(s):

Report Date:


Pagination or Media Count:



This report provides a systematic analysis of dispersion measures of shot groups from firearms. A dispersion measure is a random variable, and if its probability distribution is known with sufficient accuracy, then it can be used to make a sound statistical inference on the unknown, population standard deviations of the x and y impact-point positions. The dispersion measures treated in this report are the univariate measures range, mean deviation, and standard deviation and the bivariate measures extreme spread, mean radius, and radial standard deviation. Analysis is presented as applied to one, n-round shot group and then is extended to treat multiple, n-round shot groups. A dispersion measure for multiple, n-round shot groups can be constructed by selecting one of the dispersion measures listed above, measuring the dispersion of each group, and averaging the dispersion over groups. This procedure was followed except for the construction of dispersion measures based on the standard deviation and radial standard deviation of multiple n-round shot groups, for which we used the root mean square of the dispersion measure over groups. For each dispersion measure, tables of means, standard deviations, and percentiles were computed for single, n-round shot groups n 2-30, as well as for treatments of various k multiples k 2-5, 10 of n-round shot groups n 2-5, 10, 25. The percentile tables provided in this report are to a considerable extent unavailable elsewhere, and their inclusion is of practical interest to those developing requirements or tests on firearms precision.

Subject Categories:

  • Statistics and Probability
  • Guns

Distribution Statement: