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16 Sep 2014, 01:45
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What is the median of data set A?
(1) No number in data set A is less than the average (arithmetic mean) of the set.
(2) The average (arithmetic mean) of data set A is equal to the range of the set.
(1) No number in data set A is less than the average (arithmetic mean) of the set.
(2) The average (arithmetic mean) of data set A is equal to the range of the set.
16 Sep 2014, 01:45
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Official Solution:
What is the median of data set A?
(1) No number in data set A is less than the average (arithmetic mean) of the set.
Since no number is less than the average, it follows that no number is more than the average, suggesting that all elements in the set are identical: A = {x, x, x, ...}. This implies that the average equals the median. However, the actual value of \(x\) remains unknown, so this statement is insufficient.
(2) The average (arithmetic mean) of data set A is equal to the range of the set.
This statement is also insufficient on its own. For instance, if A = {0, 0, 0, 0}, the median is 0, but if A={1, 2, 2, 3}, the median is 2.
(1)+(2) From (1), we know that the set contains identical elements. The range of any such set is 0. Therefore, from (2), we get that (the average) = (the range) = 0. And since from (1), we have established that (the average) = (the median), it follows that (the median) = 0. Sufficient.
Answer: C
What is the median of data set A?
(1) No number in data set A is less than the average (arithmetic mean) of the set.
Since no number is less than the average, it follows that no number is more than the average, suggesting that all elements in the set are identical: A = {x, x, x, ...}. This implies that the average equals the median. However, the actual value of \(x\) remains unknown, so this statement is insufficient.
(2) The average (arithmetic mean) of data set A is equal to the range of the set.
This statement is also insufficient on its own. For instance, if A = {0, 0, 0, 0}, the median is 0, but if A={1, 2, 2, 3}, the median is 2.
(1)+(2) From (1), we know that the set contains identical elements. The range of any such set is 0. Therefore, from (2), we get that (the average) = (the range) = 0. And since from (1), we have established that (the average) = (the median), it follows that (the median) = 0. Sufficient.
Answer: C
General Discussion
08 Jan 2019, 08:05
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Hi Bunuel
Can you please explain why we consider {0,0,0,0} & {1,2,2,3} for Set A? Is repetition of elements allowed in Sets?
How a Set is different from a List?
Can you please explain why we consider {0,0,0,0} & {1,2,2,3} for Set A? Is repetition of elements allowed in Sets?
How a Set is different from a List?
