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Re: In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink]
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10 Feb 2015, 09:06
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Bunuel wrote:
In Set T, the average (arithmetic mean) equals the median. Which of the following must be true?
I. Set T consists of evenly spaced numbers. II. Set T consists of an odd number of terms. III. Set T has no mode. IV. None of the above.
A. I only B. I and II C. II and III D. I, II, and III E. IV only
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I. consider T (1, 2, 3) median=mean=2. Consider T (5, 9, 2, 19, 10) median=mean=9 II. Consider T (1, 2, 3) median=mean=2. Consider T (1, 1, 1, 1) median=mean=1 III. Consider T (1, 2, 3) mean=median=2 and there is no mode. Consider T (1, 1, 1) median=mean=1 and mode is 1.
Answer E.
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None of the proposed statements must be true; to prove this, you might consider a hypothetical: Set T could be [1,1, 3, 3], in which the average and median are both 2. This set proves I, II, and III wrong. (Note: This set has two modes, 1 and 3)
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In Set T, the average (arithmetic mean) equals the median. Which of th [#permalink]
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18 Dec 2016, 13:45
This is an Excellent Question. Here is my take on this one =>
Firstly,
Quote:
For any evenly spaced set => Mean = Median = Average of the first and the last term.
Also =>
Quote:
Sum of deviations around the mean = Zero
Now We are told that a Set T is such that its mean = median We are asked which of the statements must be true.
Statement 1--> T is evenly Spaced
Consider two sets => 5,6,7,8,9,10,11 Mean = Median=8 Now Removing 7 and 9 wont affect the mean as 8-7 will be balanced by 8-9 and the sum of deviations around 8 will still be zero. Hence 5,6,8,10,11 => Mean = 8 and Median = 8 But the above set isn't every spaced.
Hence this statement is not always true. Statement 2=>
Consider a set => 7,7,7,7 Here => Mean=Median=7 And the number of terms is even. Hence this statement also isn't always true.
Statement 3--> Consider a set => 7,7,7,7 Here Mode = 7 Hence Set T will can have a mode=> The statement isn't always true. Statement 4--> None of the above => TRUE.
None of the proposed statements must be true; to prove this, you might consider a hypothetical: Set T could be [1,1, 3, 3], in which the average and median are both 2. This set proves I, II, and III wrong. (Note: This set has two modes, 1 and 3)
So, in conclusion we can takeway from this question that for an evenly spaced set mean=median does not necessarily mean that the vice versa is true. Just because for a set mean = median does not render the set as an evenly spaced one.
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None of the proposed statements must be true; to prove this, you might consider a hypothetical: Set T could be [1,1, 3, 3], in which the average and median are both 2. This set proves I, II, and III wrong. (Note: This set has two modes, 1 and 3)
So, in conclusion we can takeway from this question that for an evenly spaced set mean=median does not necessarily mean that the vice versa is true. Just because for a set mean = median does not render the set as an evenly spaced one.
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44% (00:54) correct 
