The All Countries dataset includes land area, in square kilometers, for all 213 countries in the world. The median land area for all the countries is 94,080 sq km and the mean is 608,120 sq km with standard deviation 1,766,860.
(a) How is it possible for the mean and the median to be so different? What does this tell us about land areas of countries?
(b) If random samples of size 10 are taken from all countries of the world, what is the mean and standard deviation of the distribution of means of all such samples?
(c) If random samples of size 20 are taken from all countries of the world, what is the mean and standard deviation of the distribution of means of all such samples?
(d) Comment on your answers to parts (b) and (c): How does the sample size affect the center and variability of the distribution?