Yep, We're Skewed

All of us, especially those of us working in insurance, are constantly exposed to the results of small samples from skewed distributions. The majority of our customers will see small sample results below the population mean. Also, the most likely sample average value for any small sample from a skewed population will be below the mean of the skewed population being sampled. Experienced actuaries are aware of these issues. However, we have to be on guard and not fall back on easy assumptions that are appropriate for results from symmetrical distributions.