Re: S is a set with at least two numbers. Is the range of S greater than
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03 Jan 2020, 21:50
Given that S is a set with at least two members. We are to determine if the range of S is greater than the arithmetic mean.
(1) The median of the set S is negative
Statement 1 is sufficient. This is because we can have two different sets A: -7, -6, -5 and B: -7, -3, 100
Both A and B have medians that are negative, (i.e. -6, and -3) respectively. While the mean of A is -6, the mean of B is 30. The range of A is 2 while that of B is 107. Clearly the range of any set S that has a negative median will have a range greater than the mean. The mean of such a set that satisfies Statement 1 will have a mean that is either negative, in which case the range (always a positive number) is greater than the mean, or a positive number indicating that such a set has members that are widespread, and the range will be more than the mean.
Statement 2: The mean and the median are equal
Clearly statement 2 is insufficient. We can have two sets A:-7,-6,-5 and B: 5,6,7
While A has its median and mean =-6 and a range of 2, implying the range of A is greater than the mean, the median and mean of B =6 but the range of B is 2, which is less than the mean.
The answer is A.