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Statistics- Sum of Sets

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Statistics- Sum of Sets

by lavinia » Thu Sep 30, 2010 4:34 pm
The table below represents three sets of numbers with their respective medians, means and standard deviations. The third set, Set [A+B], denotes the set that is formed by combining Set A and Set B.

Median Mean Standard Deviation
Set A X Y Z
Set B L M N
Set [A + B] Q R S

If X - Y > 0 and L - M = 0, then which of the following must be true?

I. Z > N
II. R > M
III. Q > R

I only
II only
III only
I and II only
None
[spoiler]
Answer:E[/spoiler] Source:MGMAT
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by neerajkumar1_1 » Thu Sep 30, 2010 6:35 pm
lavinia wrote:The table below represents three sets of numbers with their respective medians, means and standard deviations. The third set, Set [A+B], denotes the set that is formed by combining Set A and Set B.

Median Mean Standard Deviation
Set A X Y Z
Set B L M N
Set [A + B] Q R S

If X - Y > 0 and L - M = 0, then which of the following must be true?

I. Z > N
II. R > M
III. Q > R

I only
II only
III only
I and II only
None
[spoiler]
Answer:E[/spoiler] Source:MGMAT
Given x>y and L = M
this means that while set A is not equally spaced, set B is equally spaced..

getting to the statements
1) Z > N ?

This definitely does not have to be true...
when we say that set B is equally spaced... we dont mean that the set will be consecutive integers e.g 1 ,2 ,3 ...

it could equally spaced multiples of 5 or 7 ....

and as for set A, it could have just 3 set of numbers e.g 1 3 4 where the standard dev would be less...

Hence we can have a case where SD of set B > SD of set A or N > Z
take for example set B as 100 200 300 500 600 and set A as 1 3 4


Statement 2) R > M

R > M can only be decided if we have a relation between Y & M

as adding a number greater than the mean will increase the overall mean
and subtracting a number lesser than the mean, will reduce the overall mean...

since we dont know what Y and M are... or the relation between them, we cant deduce anything...

Statement 3) Q > R

Again, this depends on the actual elements of the set

By the similar logic, I have given for statement 2, u can have different possibilities for Q and R


none can be said for sure...

i would choose E:none
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