1. 10 samples can be drawn from the set of 5:
5, 6, 12: mean=7.67 (23/3)
5, 6, 18: mean=9.67 (29/3)
5, 6, 20: mean=10.33 (31/3)
5, 12, 18: mean=11.67 (35/3)
6, 12, 18: mean=12.00 (36/3)
5, 12, 20: mean=12.33 (37/3)
6, 12, 20: mean=12.67 (38/3)
5, 18, 20: mean=14.33 (43/3)
6, 18, 20: mean=14.67 (44/3)
12, 18, 20: mean=16.67 (50/3)
2. The sampling distribution for the means shows a rise from 7.67 to 16.67 for the 10 samples. there are no duplications. We now have a set of 10 numbers and we can find the mean of these: 12.2, which is the same as the population mean. The median is halfway between 12 and 12.33: 12.17 (73/6), very close to the mean, indicating a non-skew distribution, that is, approximating a normal distribution.
3. We could construct a probability distribution based on either the mean or the median. If we use the median, we can work out the probability of each median value. But if we use the mean, the probability will be the same (1/10=0.1) for every mean value, since there are no duplicates.
There are only 3 median values: 6, 12 and 18. There are 3 values of 6 and 3 of 18, but 4 of 12, so the probability of 6=3/10=0.3, probability of 12=4/10=0.4, and the probability of 18=3/10=0.3. This is the probability distribution based on the median. Note that the population median is also 12.