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Set S consists of the following unique integers: -2, 17, 3,

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AnkitK
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Set S consists of the following unique integers: -2, 17, 3, [#permalink] New post   23 Jul 2011, 02:33
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Set S consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set S?

A) 1
B) 9
C) 14
D) 17
E) It Cannot Be Determined
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A
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Re: Set S consists of the following unique integers: -2, 17, 3, [#permalink] New post   27 May 2015, 21:41
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Hi All,

Whenever a question asks you to deal with the MEDIAN of a group of numbers, you MUST put the numbers in order from least to greatest (or at the very least, "group off" the numbers so that you can restrict the potential value of the median).

Here, we have 8 values (one of the values is the variable N). We're told that the values are UNIQUE, so N CANNOT be any of the other 7 values listed. We're asked which of the following answers COULD be the median, so if we determine that one of the answer choices is a POSSIBLE median, then we can stop working....

Since the group includes 8 values, the median will be the AVERAGE of the 4th and 5th values...

Putting the 7 numbers in order, we have:

-27, -3, -2, 2, 3, 15, 17

This means that the "2" will either be the 4th term or the 5th term (depending on the value of N).

IF....
N is REALLY BIG, then the 4th and 5th terms will be 2 and 3, so the median will = 2.5
N is REALLY SMALL, then the 4th and 5th terms will be -2 and 2, so the median will = 0

Neither of those answers is among the choices though, so N must be something relatively "close" to 2.....

IF....
N = 0, then the 4th and 5th terms will be 0 and 2, so the median will = 1. That answer IS among the choices, so we're done.

Final Answer:
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A


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Re: median concept [#permalink] New post   23 Jul 2011, 02:41
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if n= 0

then -27,-3,-2,0,2,3,15,17

median is =1
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Re: median concept [#permalink] New post   23 Jul 2011, 08:11
AnkitK wrote:
Set S consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set S?
A) 1
B) 9
C) 14
D) 17
E) It Cannot Be Determined


-27,-3,-2,[highlight][-1,0,1][/highlight],2,3,15,17

If n=-1; Median=0.5
If n=0; Median=1
If n=1; Median=1.5
For any other value of n;
Median is either: 0 OR 2.5

Only 1 fits.

Ans: "A"
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Re: median concept [#permalink] New post   24 Jul 2011, 09:34
we can work backwards here - only 1 fits the bill otherwise all other numbers make too big median values (after rearranging the values given)
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Re: Set S consists of the following unique integers: -2, 17, 3, [#permalink] New post   27 Jan 2017, 11:02
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AnkitK wrote:
Set S consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set S?

A) 1
B) 9
C) 14
D) 17
E) It Cannot Be Determined


Let’s order the numbers from least to greatest, excluding n:

-27, -3, -2, 2, 3, 15, 17

Including n, we have 8 numbers, so the median will be the average of the 4th and 5th numbers in our set.

Starting with answer choice A, we see that 1 COULD BE the median of the set. If n were 0, then our list would be:

-27, -3, -2, 0, 2, 3, 15, 17

Since the values of 0 and 2 are the 4th and 5th values of the set, respectively, the median is (0 + 2)/2 = 1.

Answer: A
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Re: Set S consists of the following unique integers: -2, 17, 3, [#permalink] New post   18 Mar 2018, 07:36
I had a question- it's no where mentioned that the median has to be an integer. So without knowing the value of n, how can we determine the median. Just because n=0 gives us an option as the answer, doesn't mean n=0.
n=1 Median=1.5
n=100, Median=2.5
n= -100, Median=0

Hence isn't it this case the median can not be determined here?
Am I missing something?
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Re: Set S consists of the following unique integers: -2, 17, 3, [#permalink] New post   18 Mar 2018, 07:39
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soniabhishek wrote:
I had a question- it's no where mentioned that the median has to be an integer. So without knowing the value of n, how can we determine the median. Just because n=0 gives us an option as the answer, doesn't mean n=0.
n=1 Median=1.5
n=100, Median=2.5
n= -100, Median=0

Hence isn't it this case the median can not be determined here?
Am I missing something?


Notice that the question asks: which of the following COULD be the median of set S?
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Re: Set S consists of the following unique integers: -2, 17, 3, [#permalink] New post   18 Mar 2018, 07:49
Bunuel wrote:
Notice that the question asks: which of the following COULD be the median of set S?


Thanks for responding.

"Cannot be determined" is one of the options. We are in no way determining the value of 'n' to be 0 and the median as 1.
So shoudlnt' that be the correct answer.

Also in such questions, 'could' becomes the driving word? I just want to be clear as to what should be done in case such a question shows up in exam.
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Set S consists of the following unique integers: -2, 17, 3, [#permalink] New post   18 Mar 2018, 07:52
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soniabhishek wrote:
Bunuel wrote:
Notice that the question asks: which of the following COULD be the median of set S?


Thanks for responding.

"Cannot be determined" is one of the options. We are in no way determining the value of 'n' to be 0 and the median as 1.
So shoudlnt' that be the correct answer.

Also in such questions, 'could' becomes the driving word? I just want to be clear as to what should be done in case such a question shows up in exam.


1 COULD BE the median of the set. If n were 0, then our list would be: -27, -3, -2, 0, 2, 3, 15, 17. Since 1 COULD BE the median of the set then the answer is A.
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Re: Set S consists of the following unique integers: -2, 17, 3, [#permalink] New post   07 May 2018, 19:11
AnkitK wrote:
Set S consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set S?

A) 1
B) 9
C) 14
D) 17
E) It Cannot Be Determined



We have total 8 terms , hence the median is middle most value i.e., \(\frac{(4th term+5th term)}{2}\)
Lets arrange whats given: A -27 B -3 -2 C 2 3 D 15 E 17 ( pls refer pic for clarification)
where , A B C D E are place holders for n.

Now all the cases where n is at A /B/ D/ E, the 4th term is -2 & the 5th term is 2. And hence the median is \(\frac{(-2+2)}{2}= 0\)

Now, When n is at C , n become the 4 th term. Thus the median is \(\frac{(n+2)}{2}\)

Now at C , (as n is integer & unique to the set provided ), n could assume 3 values : -1, 0 , or 1
When n=-1, the median is \(\frac{(-1+2)}{2}= \frac{1}{2}\)
When n=0, the median is \(\frac{(0+2)}{2}= 1\) .......................only one that matches the options provided
When n=1, the median is \(\frac{(1+2)}{2}= \frac{3}{2}\)

Hence, I would go for option A.
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Re: Set S consists of the following unique integers: -2, 17, 3, [#permalink] New post   26 Jul 2023, 21:47
Let us first arrange the data in ascending order ignoring n => -27 , -3, -2, 2, 3, 15, 17

Let us suppose -2<n<2

In that case median = (n+2)/2

=> 0<median<2

Let us suppose 2<n

In that case median = (-2+2)/2

=> median = 0

Among the options only A matches hence A
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Re: Set S consists of the following unique integers: -2, 17, 3, [#permalink] New post   31 Jul 2023, 12:04
If solution range from 0 to 2.5 occurs and not a single fixed value, why do we not choose the option " Cannot be determined"
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Re: Set S consists of the following unique integers: -2, 17, 3, [#permalink] New post   31 Jul 2023, 14:08
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mitranevergivesup wrote:
If solution range from 0 to 2.5 occurs and not a single fixed value, why do we not choose the option " Cannot be determined"


Hi mitranevergivesup,

Here, we have 8 values (one of the values is the variable N). We're told that the values are UNIQUE, so N CANNOT be any of the other 7 values listed. We're asked which of the following answers COULD be the median, so if we determine that one of the answer choices is a POSSIBLE median, then we can stop working....

With a little bit of work, you CAN prove that one of those four numbers COULD be the median of the group (I've shown how, in my explanation above).

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Re: Set S consists of the following unique integers: -2, 17, 3, [#permalink]
31 Jul 2023, 14:08
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