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Mean/Median

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Mean/Median

by ashforgmat » Wed May 12, 2010 9:59 pm
126) Last month 15 homes were sold in Town X. The average sale price of the houses was $150,000 and the median sales price was $130,000. Which must be true?
At least 1 house sold for > $165,000
At least 1 house sold for > $130,000 but < $150,000
At least 1 home sold for < $130,000
a. I
b. II
c. III
d. I and II
e. I and III


Please can tell the Explanation for this?
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by sanju09 » Thu May 13, 2010 3:34 am
ashforgmat wrote:126) Last month 15 homes were sold in Town X. The average sale price of the houses was $150,000 and the median sales price was $130,000. Which must be true?
At least 1 house sold for > $165,000
At least 1 house sold for > $130,000 but < $150,000
At least 1 home sold for < $130,000
a. I
b. II
c. III
d. I and II
e. I and III


Please can tell the Explanation for this?
To check the first statement, let's take the worst case to deny this, that is exactly 8 houses were sold at the median value, $130, 000, and all of the remaining 7 houses were sold at the maximum offered value, $165, 000, then 8 × $130, 000 + 7 × $165, 000 divided by 15 is less than the given mean. Since, we cannot increase the lower half beyond $130, 000 to match the given mean; all we need to believe is that, at least one house must be sold for more than $165, 000 to match the given mean. Hence, (I) must be true.

We have just seen the worst scenario above, which doesn't prove the other two statements, (II) & (III) as must to hold the stem contents true.

[spoiler]Hence, A[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



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