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# S is a set containing 9 different numbers. T is a set

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S is a set containing 9 different numbers. T is a set [#permalink]  12 Aug 2008, 10:07
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S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true? \

a) The mean of S is equal to the mean of T
b) The median of S is equal to the median of T
c) The range of S is equal to the range of T
d) The mean of S is greater than the mean of T
e) The range of S is less than the range of T
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Re: PS: Mean/Median [#permalink]  12 Aug 2008, 10:30
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E. Assuming a set cannot contain anything but integers.

vksunder wrote:
S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true? \

a) The mean of S is equal to the mean of T
Take {1,2,3,4,5,6,7,8,9} for Set S => Mean is 5 so for Set t, remove number 5 and you have the same mean.
Take {1,2,3,4,6,7,8,9} for set T

b) The median of S is equal to the median of T
Again, remove number 5 and you have 4 and 6, which you need the averge of the 4th and 5th numbers, (4 and 6 respectively) for the median of set T, again median is 5 too.
c) The range of S is equal to the range of T
Again, if you remove any of the numbers EXCEPT for 1 and 9 to get Set T, you still have 1 and 9 ans your ends so the range is 8 on both.
d) The mean of S is greater than the mean of T
mean of S with 1 through 9 is 5 (9 numbers with total of 45). If you remove number 9 to make Set T, you have 8 numbers with total of 36, or an average of less than 5 (average of 5 across 8 numbers would be a total of 40, so less than that would be less than 5 average)
e) The range of S is less than the range of T
1 through 9 would be a range of 8. It would be impossible to have Set T to be within Set S and set S have a smaller range than set T because that would mean Set T included numbers not in set S.

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Re: PS: Mean/Median [#permalink]  12 Aug 2008, 10:38
vksunder wrote:
S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true? \

a) The mean of S is equal to the mean of T
possible :
e.g S={3,5,4} T={3,5}
b) The median of S is equal to the median of T
possible
S={2,4,6} T={2,6}
c) The range of S is equal to the range of T
POSSIBLE
S={ 1,2,3,4} T ={1,2,4 }
d) The mean of S is greater than the mean of T
POSSIBLE
e) The range of S is less than the range of T

Not possible
E.

IF T is subset of S.. then Always range of S must be equal or greather than T

e.g S={ 1,2,3,4} range 3
T={1,2,3 } range 2
T ={1,2,4 } range 3
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Re: PS: Mean/Median   [#permalink] 12 Aug 2008, 10:38
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