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18 Jan 2014, 12:28
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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
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
20 Jan 2014, 00:10
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anu1706
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!..
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!..
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)
General Discussion
18 Jan 2014, 22:24
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anu1706
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
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
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
