Suppose that, as is done in some lotteries, we sample balls from a big vessel. The vessel contains a large number of balls, each labeled with a single number, 0-9. There are an equal number of balls for each number, and the balls are continually being mixed. For this example, let's collect 10 samples of three balls each.
Each sample is formed by selecting balls one at a time and replacing each ball back in the vessel before selecting the next ball. The selection process used ensures that every ball in the vessel has an equal chance of being chosen on each selection. Assume the following samples are collected.
1, 3, 4 2, 2, 6 3, 8, 8 1, 6, 7 5, 6, 9
3, 4, 7 1, 2, 6 2, 3, 7 6, 8, 9 4, 7, 9
a. Calculate the mean of each sample.
b. Calculate the median of each sample.
c. Based on the properties of the mean and median discussed previously, do you expect more variability in the means or medians? Verify this by calculating the standard deviation of the means and medians.