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
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
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:
For
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:
And
