Question

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.)

So the first thing I did was arrange the numbers in order`x_2` = 27.5 < `x_4` = 30.3 < `x_1` = 33.1 < `x_3` = 36.3.
So I assumed the numbers had to be between 30.3 and 33.1 and it said it would be a list so I made a list
30.3, 30.4, 30.5, 30.6, 30.7, 30.8, 30.9, 31.0, 31.1,, 31.2, 31.3, 31.4, 31.5, 31.6, 31.7, 31.8, 31.9, 32.0, 32.1, 32.2, 32.3, 32.4, 32.5, 32.6, 32.7, 32.8, 32.9, 33.0, 33.1
But this is wrong, I'm not sure what to do

Answer 1

31.7

Explanation:

with an even set of data, to find the median you put them in ascending order, add the two middle values and half the result. Your two middle numbers are 30.3 and 33.1

So adding gives 63.4

Halving this `63.4/2=31.7`

so the median value of your sample is 31.7 pounds.

If you have an odd set of data, again you put them in ascending order but now your middle value is the median.

If you add another piece of data to the list the only way you will get the same median as the sample on is if the new data is 31.7 pounds. If it is <30.3 then 30.3 would be the median, if it is > 33.1 then 33.1 would be the median and if it is any value between 3.3 and 33.1 this new weight would be the new median.