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For a list of positive numbers, if the median is greater

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For a list of positive numbers, if the median is greater  [#permalink]

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New post 26 Dec 2018, 08:45
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Difficulty:

  75% (hard)

Question Stats:

33% (01:49) correct 67% (02:16) wrong based on 29 sessions

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For a list of positive numbers, if the median is greater than the average, which of the following must be true?

I. At least 50% of the numbers are smaller than the median.

II. Less than 50% of the numbers are greater than the median.

III. Median is greater than the average of the largest number and smallest number.

(A) I only

(B) II only

(C) III only

(D) I and III only

(E) None

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Re: For a list of positive numbers, if the median is greater  [#permalink]

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New post 27 Dec 2018, 08:46
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For a list of positive numbers, if the median is greater than the average, which of the following must be true?

Be careful with numbers you choose

I. At least 50% of the numbers are smaller than the median.
If there are odd numbers in the list, it is not necessary that 50% are smaller than the median
Say there are five numbers...1,1,3,3,3....average is 2.2 and median is 3, so median>average...
But there are only 2 numbers less than the median ..
2 out of 5 means just 40%.. thus not ATLEAST 50%

II. Less than 50% of the numbers are greater than the median.
If there are even numbers, it is not necessary
Take 6 numbers 1, 1, 3, 4, 4, 5....median is 3.5 and average is 3..
50% are above the median..
Therefore not necessarily true

III. Median is greater than the average of the largest number and smallest number.
Not necessarily true ..
Say the numbers are...
1,1,1,2,2,2,3...
Average is 12/7 so less than 2... Median is 2..
The average of the last number and the first number is (3+1)/2=2..
Thus median is equal to the average of the first and the last number.
Again not necessarily true.

All three are not necessarily true..

E
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Re: For a list of positive numbers, if the median is greater   [#permalink] 27 Dec 2018, 08:46
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For a list of positive numbers, if the median is greater

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