Mean-square error for the sample mean and the random estimator for 10 observations in each of four conditions.

Each point shows the result from a simulation repetition, and there are 10,000 such repetitions. Contours are bivariate kernel density estimates. The large point is the mean of MSEs across repetitions. This mean for sample means is 40% larger than the mean for the random estimator, and 63% of samples show larger MSE for the sample mean.