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11 Mar 2021, 01:15
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A
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Difficulty:
45%
(medium)
Question Stats:
56% (00:58) correct
44%
(00:49)
wrong
based on 132
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Is the standard deviation of set Q equal to 0?
(1) The average (arithmetic mean) of set Q is equal to the greatest number in Q.
(2) The median of set Q is equal to the greatest number in Q.
(1) The average (arithmetic mean) of set Q is equal to the greatest number in Q.
(2) The median of set Q is equal to the greatest number in Q.
12 Mar 2021, 01:30
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Bunuel
Is the standard deviation of set Q equal to 0?
(1) The average (arithmetic mean) of set Q is equal to the greatest number in Q. Since mean = greatest, then Q consists of all identical elements. This implies that the standard deviation is 0 (the standard deviation of a set is zero if and only the set consists of identical numbers). Sufficient.
(2) The median of set Q is equal to the greatest number in Q. Clearly insufficient: If Q = {1}, then SD = 0, but if Q = {1, 2, 2}, then SD > 0. Not sufficient.
Answer: A.
General Discussion
11 Mar 2021, 09:01
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Is the standard deviation of set Q equal to 0?
standard deviation will be zero, if set Q has all equal numbers.
Stat1: The average (arithmetic mean) of set Q is equal to the greatest number in Q.
It is possible only, if Set Q has equal numbers. So, standard deviation will be zero. Sufficient.
Stat2: The median of set Q is equal to the greatest number in Q.
then set Q = {3,3,3} or {2,3,3}, so numbers are can or not be equal. So, So, standard deviation can be zero or not Not Sufficient.
So, I think A.
standard deviation will be zero, if set Q has all equal numbers.
Stat1: The average (arithmetic mean) of set Q is equal to the greatest number in Q.
It is possible only, if Set Q has equal numbers. So, standard deviation will be zero. Sufficient.
Stat2: The median of set Q is equal to the greatest number in Q.
then set Q = {3,3,3} or {2,3,3}, so numbers are can or not be equal. So, So, standard deviation can be zero or not Not Sufficient.
So, I think A.
