I'll use the following data - it's from a previous test:

And here's a graph of that data - the blue square is the mean impact location - or the center of this group.

Here's the data corrected to 0,0. You don't need to do this to calculate the vector - but it will make this tutorial make more sense.

Here's the data again - the Standard Deviations of X and Y have been graphed - as the green triangle.

Here's the hypotenuse of the SD - OR, a line from 0,0 to the point where the X and Y standard deviations land

Here's the vector displayed as a radius of a circle. In theory that circle should encompass 68% of the shots. In this case it contains 15 of the 22 shots - which, happily, is 68% of them.

Here's a graph with a circle with a radius of 2x the vector. Theoretically, this circle should encompass 95% of all shots ever fired by this setup. We have none outside - but that's because we don't have a large enough sample.

hope this helps.

**Edited by brycelarson, 29 July 2009 - 03:00 PM.**