Median of a set containing unknown values?

Question

Hi,

I was reading mgmat quant statistics chapter wherein i am not able to understand the median of an unknown value type. can somebody please tell how to go about in these set of questions?

anuj

brianlange77 · Answer

Anuj:

More than happy to help out -- the thing that is unique about medians is that you often don't need to know all of the numbers in a set to still figure out what the median is. For example, if I gave you this set of numbers (x, 4, 5, 7, 7, 9, 11) and you are told that they are all integers -- no matter what 'x' is -- the median is still 7. If x is 0, median is 7. If x is 100, median is 7. if x is 7.. guess what.. median is 7!!

Does that answer your question?

-Brian

anu1706 · Answer

Sorry but that not precisely my question was!! i can understand median is middle number in odd and avg. of 2 middle in even set of data points. 
What I want to ask is  how unknown value will effect the median of a set. .Please explain what this means.:

Extract from manhattan "Consider the unordered set {x, 2, 5, 11, 11, 12, 33}. No matter whether x is less than 11,
equal to 11, or greater than 11, the median of the resulting set will be 11.  Why? 
By contrast, the median of the unordered set {x, 2, 5, 11, 12, 12, 33} depends on x. If x is 11 or less, the
median is 11. If x is between 11 and 12, the median is x. Finally, if x is 12 or more, the median is 12.  Explain!..

KarishmaB · Answer

Notice how the two given sets are different. Ignoring x from the sets, the first set has two 11s in the middle (3rd and 4th terms) while the second one has an 11 and a 12 in the middle.

Consider {2, 5, 11, 11, 12, 33}
We need to add a term 'x' in this set and then find out the median. x can take any value and to find the median, we will put x in the set such that all terms are in ascending order. The middle term (fourth term) of this set will be the median.
Depending on the value of x, several scenarios are possible. Let's give some values to x and see the various scenarios.
x = 1; { 1 , 2, 5, 11, 11, 12, 33} (median 11)
x = 3; {2,  3 , 5, 11, 11, 12, 33} (median 11)
x = 9; {2, 5,  9 , 11, 11, 12, 33} (median 11)
x = 11; {2, 5, 11,  11,  11, 12, 33} (the only way x can be in the middle of the two 11s is if it is 11 too.
x = 12; {2, 5, 11, 11,  12 , 12, 33} (median 11)
x = 25; {2, 5, 11, 11, 12,  25 , 33} (median 11)
x = 50; {2, 5, 11, 11, 12, 33,  50 } (median 11)

Fourth term will be the median. The only time the fourth term (middle term) will be x will be when x is 11. Hence, whatever the case, the median will always be 11.

Consider {2, 5, 11, 12, 12, 33}
Again, depending on the value of x, several scenarios are possible. Let's give some values to x and see the various scenarios.
{ 1 , 2, 5, 11, 12, 12, 33} (median 11)
{2,  3 , 5, 11, 12, 12, 33} (median 11)
{2, 5,  9 , 11, 12, 12, 33} (median 11)
{2, 5, 11,  11.2,  12, 12, 33} (if x is in the middle of 11 and 12, it can take many values such as 11.2/11.7 etc and that will be the median)
{2, 5, 11, 12,  12 , 12, 33} (median 12)
{2, 5, 11, 12, 12,  25 , 33} (median 12)
{2, 5, 11, 12, 12, 33,  50 } (median 12)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Median of a set containing unknown values?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards