Comparison of estimators
Most estimators that are used in statistics have error distributions that are centred on zero — they are unbiased. The standard errors of the estimators are therefore the most important way to compare their accuracy.
Comparison of mean and median
We will use a simulation to investigate whether the mean or median is the better estimator of the mean, µ, of a normal distribution. Samples of 20 values were selected from a normal population with mean µ = 1000. The stacked dot plot on the left below shows the errors when the mean was used to estimate µ, and the corresponding errors when the median was used are shown on the right.
Since the errors for the sample mean tend to be closer to zero than those for the median, we conclude that the sample mean is a better estimator of µ then the median.
This comparison can also be based on the standard deviations of these distributions — the standard errors of the two estimators.