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18 Aug 2006, 04:16
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Please explain.
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18 Aug 2006, 06:11
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I must be true, II and III can obviously be false
If we think of the house prices in ascending order a1, a2, a2....a15
and the call the mean m
We can use the fact that D= (a1-m)+(a2-m)+...+(a15-m)=0
(The sum of the deviations of the elements from the mean must be 0)
We know that a1,a2....a8 are at most 130,000
So (a1-m)+(a2-m)+...+(a8-m) is less than -20,000(8)=- 160,000
Suppose no house sold for more than $165k
Then (a9-m)+...(a15-m) is at most 15,000(7)=105,000
And D is less than -55,000, which cannot be true.
Therefore, at least one house sold for more than $165k
If we think of the house prices in ascending order a1, a2, a2....a15
and the call the mean m
We can use the fact that D= (a1-m)+(a2-m)+...+(a15-m)=0
(The sum of the deviations of the elements from the mean must be 0)
We know that a1,a2....a8 are at most 130,000
So (a1-m)+(a2-m)+...+(a8-m) is less than -20,000(8)=- 160,000
Suppose no house sold for more than $165k
Then (a9-m)+...(a15-m) is at most 15,000(7)=105,000
And D is less than -55,000, which cannot be true.
Therefore, at least one house sold for more than $165k
