Probability and Statistics - one question (One paragraph should be enough to answer the question - no plagiarism please) Suppose you randomly took

Probability and Statistics - one question (One paragraph should be enough to answer the question - no plagiarism please)

Suppose you randomly took 10,000 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?

(This question is in relation to the book Understanding Statistics in Behavioral Sciences. 10th ed. 9781111837266)