Answer
a)
56, 1/16
52.5, 2/16
57, 2/16
51, 2/16
49, 1/16
53.5, 2/16
47.5, 2/16
58, 1/16
52, 2/6
46, 1/16
b) $53.5$
c) No
Work Step by Step
a) We know there are $4$ numbers, so there are $4^2=16$ ways to combine them. Combining the values with the same median, we obtain the following:
Median, probability:
56, 1/16
52.5, 2/16
57, 2/16
51, 2/16
49, 1/16
53.5, 2/16
47.5, 2/16
58, 1/16
52, 2/6
46, 1/16
b) We can see that the population median of this set is $53.5$
c) The population median is biased, because it is not equal to the sample median.
