If M is a negative integer and K is a positive integer, which of the following could be the standard deviation of the set
{-7,-5,-3,M,0,1,3,K,7} ?
1. -1.5
2, -1
3. 0
A) 1 only
b) 2 only
c) 3 only
d) 1 & 3 only
e) None
K+M-4/9 = Mean
now K = { 4,5,6}
M can be ={ -3,-2,-1}
I could not proceed from here ... picking up these numbers to put in S.D formula is just way too time taking.
I am sure there must be a quicker way !
Experts please help.
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- prachi18oct
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Hi prachi18oct,prachi18oct wrote:If M is a negative integer and K is a positive integer, which of the following could be the standard deviation of the set
{-7,-5,-3,M,0,1,3,K,7} ?
1. -1.5
2, -1
3. 0
A) 1 only
b) 2 only
c) 3 only
d) 1 & 3 only
e) None
K+M-4/9 = Mean
now K = { 4,5,6}
M can be ={ -3,-2,-1}
I could not proceed from here ... picking up these numbers to put in S.D formula is just way too time taking.
I am sure there must be a quicker way !
Experts please help.
The question is not of the GMAT standard. Since Standard deviation is always positive, options A, B and D are ruled out.
SD can either be positive or 0.
Two things are not clear from the question narration: 1. Are the integers in the set {-7,-5,-3,M,0,1,3,K,7} arranged in the ascending order? The way they are arranged, it suggests that they; however, we cannot assume this. The question must tell it. 2. Are M and K unique? As per your work (K = {4,5,6}, M = { -3,-2,-1}), only K is unique.
Having said that there is no need to know whether K and M are placed in an order in the set or they are unique. The SD of the set cannot be 0 since there are many unequal numbers in the set, making SD a positive number. Since there no option as a positive number, the correct answer is none.
The correct answer: E
Hope this helps!
Relevant book: Manhattan Review GMAT Sets & Statistics Guide
-Jay
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One way of thinking about it:
The SD is NEVER negative, no matter what the set, and the SD = 0 if and only if all the terms in the set are the same.
Since there are different terms in this set, 0 is impossible, and all the negative answers are always impossible.
The SD is NEVER negative, no matter what the set, and the SD = 0 if and only if all the terms in the set are the same.
Since there are different terms in this set, 0 is impossible, and all the negative answers are always impossible.