Sample Median, Stats help?

A sample consisting of four pieces of luggage was selected from among those checked at an airline counter, yielding the following data on x = weight (in pounds).
x1 = 33.1, x2 = 27.5, x3 = 36.3, x4 = 30.3
Suppose that one more piece is selected and denote its weight by x5.
Find all possible values of x5 such that x = sample median.
(Enter your answers as a comma-separated list.)

I keep getting is 31.8 but it's wrong. I know it says all to write all possible answers, but this is the only one I know

1 Answer
Mar 28, 2018

We first order by weight:

Explanation:

27.5 -- 30.3 -- 33.1 -- 36.3

Since there is an even number of suitcases the median is now the average of the two middle numbers:

#MED=(30.3+33.1)/2=31.7#

For #x5# to be the median, it should be third in weight. this can vary from #30.3# to #33.1# pounds, or any value in between.
The two ordered lists for the extremes would then be:
27.5 -- 30.3 -- 30.3 -- 33.1 -- 36.3 and:
27.5 -- 30.3 -- 33.1 -- 33.1 -- 36.3
(median = middle = third = bold)

Conclusion:
#x5# can have any value from #30.3->33.1# (inclusive), or #30.3<=x5<=33.1#
And #x5# would then still end up in the middle of the list.