Set S consists of even number of integers. Is the median of

Question

Set S consists of even number of integers. Is the median of set S negative ?

1 . Exactly half of all the elements of set S are positive. 

2. The biggest negative element of set S is -1.

sumande · Answer

This should be E.

Stmt 1: insufficient. 
S={-1,0,1,2}; Median=0.5
S={-2,-1,1,2}; Median=0

Stmt 2: insufficient. 
We don't know how many elements are there in the set.

Both together, I am confused. What does "biggest negative element" mean? -1 > all other negative integers, so there can be any other negative element in the set. Or is the definition of biggest in terms of the absolute value. However, in either case it will be insufficient.
S={-1,4}; S={-1,1} Different medians.

racha24 · Answer

if you combine both statements medial will always be greater than or equal to 0. C.

sumande · Answer

That depends on the definition of "biggest number". -1 is bigger than -4, so we can have a -4 in the set. But considering absolute values, we cannot. Then the answer will be C. (I shouldn't solve these too early in the morning. :-D

) But otherwise the answer should be E. Am I making any sense? (I have a feeling, I am not.)

bkk145 · Answer

I'll go with C

It would be C if we consider half elements positive and half negative
Say S={-1,1} or S={-6,-1,1,1} will give you a median of either 0 or positive number; thus, can never be negative.

If we consider half positive, some zeros, some negative, you get the same result that median can never be negative.

eschn3am · Answer

good question. I'll go with C. That largest negative number being -1 is the key.

sumande · Answer

My question still is "how do you define the largest negative number?"

eschn3am · Answer

Absolute values have nothing to do with this.

The median is the average of the middle two numbers. Since half the numbers are positive we know that we are averaging some number with a number >= 1. If the biggest negative number of set S is -1 that means you would average 1 (or more) and -1 and you'd get >= 0. if you averaged 1 and 0 you'd get > 0. there's no way to average them and get less than 0. so it's C.

im sorry if this isn't what you're asking. I'm rather confused on what exactly your question is

sumande · Answer

Thanks for attempting to understand my vague question. :-D

My confusion is simple. The question says the biggest negative value is -1. So does that mean that -4 or -5 or -99 cannot be part of the set ?? For me they are lesser than -1. So, the biggest value being -1 does not tell us anything. Forget about the absolute value thing, it was too early in the morning. :-D

eschn3am · Answer

No, you're right here. The biggest negative value is -1 so the other one can be -100, -50, -23523523 or 0. It doesn't matter. They are asking for the MEDIAN of the set, not the average. The median is the middle term of a set (when there are an odd number of elements) or the average of the middle two elements if a set has an even number of elements (like this one). That means the sets can look like any of these

{-235, -1, 1, 23}
{-2, -1, 1, 2}
{-1, 0, 1, 2}

all we know is that two integers (the two on the right if you list them by size) must be positive. The smallest number can be anything it wants, but the largest negative number is for sure -1. so you could have 0, -1 or -25, -1. 

but the average of the two center terms will ALWAYS be a positive number (or at the lowest, 0). The median of the set will never be negative. so you get C.

sumande · Answer

Stupid me...I was imagining the set without -1 !! :shock:

eschn3am · Answer

That would do it! lol

If exactly half the numbers are positive that means the other ones must be 0 or negative. either way it works out to be a positive median

Fistail · Answer

using 1 and 2: the lowest median could be 0, which is not -ve.

so its C.

Set S consists of even number of integers. Is the median of

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