Nsentra wrote:

median vs average

don't forget to show your reasoning !

my understanding is that for a set S = {10, 10, 10 , 20, 25}

mean = 15

median = 10

so median can be equal to the lowest value of a set.

hence, statement III need not be true.

statement II - even if there is no value between 130,000 and 150,000 , it is possible to have that difference accounted for by another value. lets say a home was sold for 130,000 after listing for 145,000. another home can be sold for 15,000 more to make this up and not lower the mean.

statement I - mean is 150,000 , implying that, on average, for every home that is sold for 150,000 -x , another has to be sold for 150,000 +x

given median is 130,000 , we know that this is the value of the 8th home when all home values are arranged in ascending order.

to prove that no home sold for more than 165,000 , we need to assume the highest value possible for the first 8 homes discussed above. hence 8 homes sold for 130,000 each.

now, the remaining 7 homes have to 'cover the lost ground' ie 150,000-130,000 = 20,000 per home ie 160,000 for the 8 homes.

ie to maintain the mean, each of these 7 homes , on average, has to sell for 150,000 + 160,000 /7 = 150,000 + 22,000 appx = 172,000 appx

if all of these 7 sell for a maximum of 165,000 , the mean of 150,000 cannot be achieved. that contradicts a given fact.

hence I has to be true