Question

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

Answer 1

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.