Thinking about this in terms of a Gaussian distribution, is a 1 MOA gun one which shoots 2 std deviations within 1 MOA? 3 std deviations? A simple 5 round group

Thinking about this in terms of a Gaussian distribution, is a 1 MOA gun one which shoots 2 std deviations within 1 MOA? 3 std deviations? A simple 5 round group seems like it would provide some information, but not enough to fully characterize the distribution.