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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.
(1) Set N contains the median of set M.
(2) The range of set M and set N are equal.
27 Mar 2020, 07:15
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Bunuel
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.
(1) Set N contains the median of set M.
(2) The range of set M and set N are equal.
OFFICIAL EXPLANATION
(B): Standard deviation is a measure of the “spread” of a group of numbers.
(1) INSUFFICIENT: If set M contains the numbers {1, 2, 3, 4, 5, 6, 7}, then 4 is the median. Set N could be {3, 4, 5}, which has a smaller standard deviation than set M because the two sets have the same average but N is not as spread out as M.
Alternatively, N could be {1, 4, 7}, which has a larger standard deviation than set M because the two sets still have the same average, but N is now more spread out than M. (It doesn't have additional values that are closer to the average.)
(2) SUFFICIENT: If set M contains the numbers {1, 2, 3, 4, 5, 6, 7}, and set N has the same range, then N must contain 1 and 7. If set N contains {1, 4, 7}, then N has a larger standard deviation than M. If set N contains {1, 2, 7}, the standard deviation actually increases even more (because the numbers are no longer evenly distributed}. No matter what combination you try, the standard deviation of N has to be greater than the standard deviation of M.
The correct answer is (B).
General Discussion
27 Mar 2020, 07:00
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Bunuel
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.
(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
(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
(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 B
But another set that we can take here specifically is
Let M be {2,2,2,2,2,2,2} as in the stem it is mentioned
Bunuel
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
(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
(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 E
Bunuel - Please suggest. Is my reasoning correct for this
