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Median/Mean

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by RikaMueller » Sun Nov 28, 2010 2:08 am
A list of measurements in increasing order 4 5 6 8 10 and x. If the Median is 6/7 times their arithmetic mean. What is value of x?

16
15
14
13
12

Pls clarify. I chose 15 but this is wrong.
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by Geva@EconomistGMAT » Sun Nov 28, 2010 2:59 am
The median for an even number of terms is the average of the two middle terms. In this case, the median will equal the average of 6 and 8, or med=7.
If the median is 6/7*mean, then
7=6/7*mean

Mean is 49/6.

Since mean is "sum of terms" / number of terms", and number of terms is 6 (which corresponds to the bottom of 49/6, it follows that x must be a term that brings the sum to 49.

4+5+6+8+10+x=49
x=49-33 = 16.
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by rishab1988 » Sun Nov 28, 2010 4:03 am
This isn't a tough question.

The of terms including x are even.

The median = avg of 2 middle terms [6 and 8] = 7

Avg = (33+x)/6

Median = 6/7 Avg [ as per question]
7 * Median = 6* Avg
7*7 = 6 * (33+x)/6
49= 33+x
x=16

or A
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