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Set S contains seven distinct integers. The median of set S

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Set S contains seven distinct integers. The median of set S [#permalink] New post 19 Sep 2010, 11:37
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Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?

A. m
B. 10m/7
C. 10m/7 – 9/7
D. 5m/7 + 3/7
E. 5m
[Reveal] Spoiler: OA
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Re: Highest possible all values in set S [#permalink] New post 19 Sep 2010, 11:48
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Orange08 wrote:
Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?
a) m
b) 10m/7
c) 10m/7 – 9/7
d) 5m/7 + 3/7
e) 5m


If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order;
If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.


So median of S, which contains seven terms is 4th term when arranged in ascending order;: median=4th \ term=m.

Now, to maximize the mean we should maximize the terms. As numbers in S are distinct integers and the highest number in S could be equal to 2m, then maximum values of the terms would be: m-3, m-2, m-1, median=m, 2m-2, 2m-1, 2m.

Mean=\frac{(m-3)+(m-2)+(m-1)+m+(2m-2)+(2m-1)+2m}{7}=\frac{10m-9}{7}.

Answer: C.
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Re: Highest possible all values in set S [#permalink] New post 19 Sep 2010, 11:52
Seven distinct integers, the highest value is equal to twice the median. To achieve the highest possible mean you need the following seven integers:

Set S = {2m, 2m - 1, 2m - 2, m, m - 1, m - 2, m - 3}

10m-\frac{9}{7}= \frac{10m}{7} - \frac{9}{7}

Answer is C
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Re: Highest possible all values in set S [#permalink] New post 19 Sep 2010, 14:28
I had missed reading distinct and made the set as m,m,m,m,2m,2m,2m and came with option B.

Phuf...why they keep such answer choices :(
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Re: Set S contains seven distinct integers. The median of set S [#permalink] New post 02 Dec 2013, 13:37
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Re: Set S contains seven distinct integers. The median of set S [#permalink] New post 05 Feb 2014, 06:21
To maximize the average we need to maximize all the distinct integers in the set.

the numbers then will be

m-3, m-2, m-1,m,2m-2,2m-1, 2m average is sum of these divided by 7.

\frac{(10m-9)}{7} = \frac{10m}{7}- \frac{9}{7}

C.
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Re: Set S contains seven distinct integers. The median of set S   [#permalink] 05 Feb 2014, 06:21
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