Suppose you randomly took 10000 samples, each of size N, from a population of scores and computed the mean, median, and mode of each sample.

Suppose you randomly took 10000 samples, each of size N, from a population of scores and computed the mean, median, and mode of each sample.  Next, you computed the variance of the 10000 mean values, the 10000 median values, and the 10000 mode values.  If you rank ordered the resulting three variances, what order would you expect?  What property of the mean and median did you use in answering this question? (No plagiarism and no more than 2 paragraphs please)