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Medians

by sensei_mike » Fri Mar 25, 2011 4:45 pm
Two sets, A and B, have the same number of elements and the same median. Which set has the higher average?

1) In Set A, 75% of the numbers are greater than or equal to the median. In Set B, 50% of the numbers are greater than or equal to the median.

-How is 1) above even possible? Isn't the definition of the median that 50% of the numbers are > the median and 50% are < the median?
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by srcc25anu » Fri Mar 25, 2011 5:11 pm
it states greater than or eqaul to ...
lets take a set A of 5 numbers (1,3,3,4,5)
here median = 3 and 4 out of 5 numbers in the set are greater than or equal to the median (or to say 80% of numbers)
so its possible for greater than equal to 50% of the numbers in a set to be equal to the median.
if the set contained all identical elements say set A = (4,4,4,5,5), then 100% or all the numbers would be greater than or equal to the median

However if given that all numbers in the set are distinct, then its not possible and what you say holds true.
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by sensei_mike » Fri Mar 25, 2011 8:13 pm
ah-ha! Thanks!! So yeah, my big miss was recognizing that multiple of the same number might be included in the set. Thanks!!
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by ankur.agrawal » Fri Mar 25, 2011 8:20 pm
sensei_mike wrote:Two sets, A and B, have the same number of elements and the same median. Which set has the higher average?

1) In Set A, 75% of the numbers are greater than or equal to the median. In Set B, 50% of the numbers are greater than or equal to the median.

-How is 1) above even possible? Isn't the definition of the median that 50% of the numbers are > the median and 50% are < the median?
As they both have the same no of elements & same median, The set which has a greater sum will have a higher average. So Set A should have a higher average.

Statement 1 should be sufficient.
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by force5 » Sat Mar 26, 2011 5:34 am
yes the given statement should be sufficient... however sensei_mike can you please post the entire question......
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by rohu27 » Sun Mar 27, 2011 8:18 am
if the st contains 4 elements,
75% would be last 3 for ex: 1 10 10 10 - 10 is the median
set B 50% would be last 2 - it can be somethign liek this - 1 10 10 200
looking at the above i dnt thnk st1 alone is suff. wht say?
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