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amamd
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 Posted: Sat Jul 05, 2008 7:17 am Post subject: X,3,1,12,8 |
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X,3,1,12,8
If x is an integer, is the median of the 5 numbers shown greater than the average?
1 x>6
2 x is greater than the median of the 5 numbers
The OS is E  , Can not figure out. Could some one help? Thanks! |
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Ian Stewart
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| Posted: Sat Jul 05, 2008 11:35 am Post subject: Re: X,3,1,12,8 |
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| amamd wrote: | X,3,1,12,8
If x is an integer, is the median of the 5 numbers shown greater than the average?
1 x>6
2 x is greater than the median of the 5 numbers
The OS is E , Can not figure out. Could some one help? Thanks! |
What could the median of the set be? We have the set {1, 3, 8, 12, x}. If x is less than 3, the median will be 3. If x is between 3 and 8, the median will be x. If x is greater than 8, the median will be 8.
What is the average of the set? (24+x)/5.
All right, let's look at the statements:
1) x > 6. This gives two possibilities. Either 6 < x <8, and x is the median, or x >=8, and 8 is the median. Let's only look at the second case, where the median is 8, and find out what must be true for the median to be greater than the average:
8 > (24+x)/5
40 > 24 + x
16 > x
If x <16, then the median will be greater than the average. If x >= 16, the median will not be greater than the average. Insufficient.
2) If x > 8, then x is greater than the median. From the work above, this is insufficient- we really want to know whether x is smaller than 16.
Together, they're still insufficient; we still don't know if x is larger than 16.
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ildude02
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| Posted: Sat Jul 05, 2008 5:59 pm Post subject: |
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Nice explanation, Ian. I might add, as always  |
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