I recently received a proposed total loss settlement for an auto from my insurance company based on an average of three "corrected" values based on local list prices for the same vehicle.
How the insurer arrived at the "corrections" is a separate issue. What I am disputing is the number of vehicles used in the "average".
Essentially, I am arguing that they need to account for confidence limits in their calculation of the average. If they are averaging only three values of, say, $9,000, $10,000, and $8,000, it is possible that if they pick 3 other vehicles with values of $15,000, $20,000, and $10,000, they would get a much different result.
The 95% upper confidence limit on the mean is the sample mean plus around twice the sample standard deviation of the samples presented. For the first example above, the sample average is $9,000 and the sample standard deviation is $817. Thus I would argue that a more accurate estimate of the average value is $9,000 + $1,600 ($10,600), not the straight sample average of $9,000 that they are proposing.
Is there any precedent for this kind of argument in any Texas or Federal Courts?