Ragged holes

It is possible — and with larger shot groups and/or more precise rifles increasingly likely — that the target will exhibit a "ragged hole" into which one or more shots has disappeared. In statistics this is known as a "center-censored" sample. A detailed explanation and discussion of the problem is here. This frustrates the direct calculation of Invariant Measures like Mean Radius and Variance, which require the location of each and every shot on a target. Alternatives:

• Range Statistics can still be measured directly from a center-censored target.
• Order Statistics can also provide good estimates of precision in most cases.
• Another alternative is to use CEP to back into an estimate of σ:
  1. Find the radius r of the smallest circle that covers the ragged hole.
  2. From n, the number of shots fired, and c the number outside the circle, calculate the proportion of shots inside that covering circle p=(n-c)/n. This turns the target into a sample with CEP(r).
• Avoid ragged holes by shooting fewer shots per target (meaning per "point of aim" since some paper targets have more than one POA), and then aggregate them into a data set. Software to automate this process exists, e.g. OnTarget Target Data System offers coded target sheets that can be scanned to automatically aggregate shots across multiple aiming points.