hazpazfaz wrote:7 houses under 130.000 and 7 houses above
I: It could be that all of the below-median houses are 129.999 and that could mean that above-median houses are all below 165.000
II: It could be that all below-median houses are 1, therefore al below median houses have to be > 150.000 to get the mean provided
III: A median of a odd number N implies that there are (N-1)/2 under the median --> (15-1)/2= 7 so there are 7 numbers below 130.000.
C
I think you made a slightly mistake. median 130.000 means 7 houses under or equal 130.000 and 7 houses above or equal 130.000
Since this is a must be true problem you have to try to find counterexamples
I) At least 1 house sold for > $165,000
we want to prove that all the houses have been sold by less than 165.000.
so let's maximize the value of the houses that are below the median (130.000) giving them a value of 130.000 now we have 8 houses with a value of 130.000 and the mean has to be 150.000, so the price of other 7 house have to account for this difference (20.000 *8 + 150.000 *7).
the medium price of the houses would be (20.000 *8 + 150.000 *7)/7 = 172857 bigger than 165.000 so it has to be true.
II) At least 1 house sold for > $130,000 but < $150,000
not necessary think of the configuration of the first statement
8 houses at 130.000
and 7 at 172857
III) At least 1 home sold for < $130,000
not necessary same as II
8 houses at 130.000
and 7 at 172857
