The mean is an unbiased estimate
of the population mean regardless of the shape of the population
distribution. The median is an unbiased estimate for normal distributions
but not for skewed distributions. When the formula with N in the
denominator is used to estimate variance, the mean of the sampling
distribution is less than the population variance and is therefore
a biased estimate. The mean has less sample variability than the
median for most distributions including those with relatively large
skew. However, there are some extreme distributions for which the
median has less sample variability.