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Mean, Medium, SD Question [#permalink]
27 Mar 2007, 14:30

Hi Everyone,

This is my first post and I have a question on the following problem on mean, medium, and standard deviation:

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.

Set A ____ X (Mean) Y (Medium) Z (SD)
Set B ____ L (Mean) M (Medium) N (SD)
Set [A + B] _____ Q (Mean) R (Medium) S (SD)

If X â€“ Y > 0 and L â€“ 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

Is there a general rule that I can use to solve this quickly instead of listing out possible examples?

let's consider three sets A, B , C
A= { 1,2,3,4,5,7,7} X=29/7=4.14, Y=4, Z >0
B={6,6,6,6} L=6, M=6, N =0
C={1,2,3,4,5,6,6,6,6,7,7} Q=53/11 =4.81, R=6, S=

Sets satisfy the condition X-Y >0, L-M=0, Lets evaluate the options:
I. Z > N ****true****
II. R > M ****not true***
III. Q > R *****not true***

I am not sure about the I, this holds true for these sets may not be true for other sets.

let's consider three sets A, B , C A= { 1,2,3,4,5,7,7} X=29/7=4.14, Y=4, Z >0 B={6,6,6,6} L=6, M=6, N =0 C={1,2,3,4,5,6,6,6,6,7,7} Q=53/11 =4.81, R=6, S=

Sets satisfy the condition X-Y >0, L-M=0, Lets evaluate the options: I. Z > N ****true**** II. R > M ****not true*** III. Q > R *****not true***

I am not sure about the I, this holds true for these sets may not be true for other sets.

I : Z>N, from set B we may know that the medium M = Mean L, but we dont have any information about the distribution, which will indicate the standard deviation from the mean. The distribution of the elements in set B can be more diversed and deviated than the distribution of set A. hence its Z>N in inconclusive

II :R > M, R is a medium of both the sets put together, while M is the medium of set A. Neither we have any information about the range of the elements in A and B, nor we know the elements of both the set. hence comparisons of mediums of individual sets with the medium of set [A+B] put together may not result anything.

III : Inconclusive for the reasons mentioned above.