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DS: homes in town X

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Senior Manager
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DS: homes in town X [#permalink] New post 30 Oct 2006, 18:25
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median vs average
don't forget to show your reasoning !
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 [#permalink] New post 31 Oct 2006, 09:24
Was stumped by this... :oops: :cry:

Pls provide the reasoning.
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Re: DS: homes in town X [#permalink] New post 31 Oct 2006, 14:49
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
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Re: DS: homes in town X [#permalink] New post 31 Oct 2006, 16:23
Nsentra wrote:
median vs average
don't forget to show your reasoning !


I

15x150 000= 2 250 000 (total price for all 15 houses)
The price of the 8th house=130 000

Let's assume that the first 8 houses cost 130 000 each, and the rest of the houses cost 165 000 each (those are the highest possible values per house that do not exceed 165 000). The sum of the prices of those houses is 2 195 000, which is less than 2 250 000 => At least one of the houses costs more than 165 000. YES

II

For sure there is at least one house that costs more than 130 000, BUT it is not necessary the price of any of the houses to be below 150 000. NO

III

Since the first 8 houses may cost 130 000 each, and 130 000 will still be the median price, it is not necessary the price of any of the houses to be below 130 000. NO

Answer: I
Re: DS: homes in town X   [#permalink] 31 Oct 2006, 16:23
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