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my initial concern was whether we can infer that a+b is the median but i overlooked the fact that we needed a number, not the expression (because a+b, where a and b are both zero, implies all the 3 terms, a-b, a+b, a-b are also zero.) _________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

my initial concern was whether we can infer that a+b is the median but i overlooked the fact that we needed a number, not the expression (because a+b, where a and b are both zero, implies all the 3 terms, a-b, a+b, a-b are also zero.)

just to clarify: a and b don't have to be equal to zero, b = -a satisfies the condition of a+b being the mean of the set. However, for each (a,b) such that b = -a, a+b = 0 and it is going to be the median of the set.

my initial concern was whether we can infer that a+b is the median but i overlooked the fact that we needed a number, not the expression (because a+b, where a and b are both zero, implies all the 3 terms, a-b, a+b, a-b are also zero.)

just to clarify: a and b don't have to be equal to zero, b = -a satisfies the condition of a+b being the mean of the set. However, for each (a,b) such that b = -a, a+b = 0 and it is going to be the median of the set.

yea, understood. b-a and a-b are "polar opposites" where they eventually net out to zero. _________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

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