Three Randomly Selected Households Are Surveyed as a Pilot Project $\mathrm { n } = 2$

Essay

Three randomly selected households are surveyed as a pilot project for a larger survey to be conducted later. The numbers of people in the households are 3, 8, and 10. Consider the values of 3, 8, and 10 to be a population. Assume that samples of size n $\mathrm { n } = 2$ 2 are randomly selected with replacement from the population of 3, 8, and 10. The nine different samples are as follows: (3, 3), (3, 8), (3, 10), (8, 3), (8, 8), (8, 10), (10, 3), (10, 8), and (10, 10).
(i) Find the median of each of the nine samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution.
(ii) Compare the population median to the mean of the sample medians. (iii) Do the sample medians target the value of the population median? In general, do medians make good estimators of population medians? Why or why not?