Q & A: Whole Number Means

Here's a question from a website visitor regarding assigning a mean value for a new QC material with the following assumptions:

"1.    The analyte reports out as a whole number.
2.    The results of calculations on 20 replicate samples are;
    A.    Mean = 10.5
    B.    SD = 0.5
    C.    2 SD Range = 9.5 - 11.5
    D.    95% Confidence Interval = 10.3 - 10.7
    E.    CV% = 4.9

The question is "what to set the mean at?" One camp contends that the mean of 10.5 should be used, even though no result will ever "hit" the mean. The other camp states that the mean should be set to 10 or 11 regardless of whether or not a LJ shows bias, or even 10x failure. "

Answer after the fold.

This is a "rounding" problem and there probably isn't a perfectly right answer, except to get an extra significant figure in the measurement.

However, in this situation, I would set the mean at 10.5 and let the data points bounce around the mean, rather than setting mean at 11 or 10.  Control limits would have to be set at 9 to 12, which will correspond to 3 SD limits.  Best not to use a 10x rule under these conditions and wouldn't use 1:4s either.  2:2s can't be implemented, so you're left with 1:3s in this application.

Note, this is similar to Dietmar Stockl's article about "pearls on a rope." When values are rounded or only reported in whole numbers, the dots accumulate in "ropes" on the chart. The solution is get more significant figures, so the values are more normal. We've also answered a similar question about "whole number" standard devations.