Bunuel wrote:
Set M contains seven integers and set N contains three values chosen from set M. Is the standard deviation of set N greater than the standard deviation of set M?
(1) Set N contains the median of set M.
(2) The range of set M and set N are equal.
Lets take a random set here,
Let M be {1,2,3,4,5,6,7}
Here median = 4
mean = 4
range = 6 (7 - 1)
Considering statement 1,
Bunuel wrote:
(1) Set N contains the median of set M.
As per statement, lets suppose N is a set of {1,4,7}
Then S.D of N is higher than S.D of M
But if N is a set of {3,4,5}
S.D. of N is equal to S.D. of N
Hence statement 1 itself is Insufficient.Considering statement 2,
Bunuel wrote:
(1) The range of set M and set N are equal.
As per statement, N has the same range as M,
So two digits out of three are already fixed, that is, 1 and 7.
Hence, lets suppose N is a set of {1,4,7} or {1,6,7} or {1,3,7}
Then S.D of N is always higher than S.D of M which is more equally distibuted as compared to N.
Hence statement 2 itself is Sufficient.That makes the answer as BBut another set that we can take here specifically isLet M be {2,2,2,2,2,2,2} as in the stem it is mentioned
Bunuel wrote:
Set M contains seven integers
Now integers may be same or different, that is not mentioned.
If we take M as {2,2,2,2,2,2,2}, then
Considering statement 1,
Bunuel wrote:
(1) Set N contains the median of set M.
Then N is {2,2,2}
Then S.D of N is equal to S.D of M
Hence statement 1 itself is Insufficient.[/color]
As we consider both the sets
Considering statement 2,
Bunuel wrote:
(1) The range of set M and set N are equal.
Then N is {2,2,2}
Then S.D of N is equal to S.D of M
Hence statement 2 itself is Insufficient.
As we consider both the sets
Considering Statement 1 and Statement 2 together, still no definite solution.
That makes the answer as EBunuel - Please suggest. Is my reasoning correct for this
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Regards,
AD
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