2 If you had data for a sample of students at LSU on the amo

2- If you had data for a sample of students at LSU on the amount of money spent in the previous year on overnight stays in a hospital, probably the median and mode would be $0 but the mean would be a positive number. Explain why. Make reference to the definitions of median, mode, and mean in your explanation. (You can use an example to explain, if you want.)

Solution

It seems that the case here is that the majority (more than half) of the respondents have spent $0.

In that case, when the expenditures are arranged from lowest to highest, the middle term has to be 0. [as more than half is 0.]

The mode also has to be 0, as no other number can be more frequent, if more than half is 0.

The mean, though, will always be positive, as if at least one spent something, that will contribute to the sum of the expenditures, and regardless how many students you divide that sum, that will still be positive.

That\'s why.