130,000 is the median

House 8 sold at 130,000

Best case: houses 1 - 8 sold at 130,000

(130'*8 + 7*x)/15 = 150'; x=173'

x = average price of houses 9-5

At least 1 house must cost more than 173' to get to that average for houses 9-15.

We do not know if any house higher than 130 and lower than 150 is sold

We do not know if any house lower than 130 is sold -> houses 1-9 could all have been sold at 130

Therefor only I correct

I'm a little confused... can you be a little elaborate?

How does this work ..anyone :

The median is the middle of a distribution: half the scores are above the median and half are below the median

If you have a sample of 15 houses: the median is the price of house #8

House #8 costs 130,000

Then, to get to the average of 150,000:

It is

[Houses 1-7 + 130000 (for house 8) + Houses 9-15 ] / 15 (=total number of houses]

The first question: is there at least 1 house sold at over 165000?

To solve it:

Highest value for houses 1-7 is if they are all sold at 130,000 (they cannot be sold higher as the median is 130000).

So you change the formulat to [8*130000 + 7*x]/15

x is the average price of houses 9-15 (i.e. the upper valued 7 houses)

Solve it for x (normal equation) and you get an average of over 170000. Therefore, there is at least one house with a price of over 165000; I is correct. This does not tell us however, how the prices are distributed. There could be a case that houses 1-8 were sold for 130000 and houses 9-15 for 172000. Therefore, II and III are not correct.