You are going to make seven observations of the data. There is a finite probability that all seven of the observations are greater than the median, and there is an equal probability that all seven observations are less than the median. Since the definition of the median of a set of data is that value such that exactly half of the values are greater and half of the values are less than the median, the probability that any given observation is greater than the median is 0.5, and the probability that any given observation is less than the median is also 0.5.
The situation is precisely the same as flipping a fair coin seven times in a row. And the question asked is what is the probability that you don't get either seven heads in a row or seven tails in a row.
You can do your own arithmetic.
John
My calculator said it, I believe it, that settles it
