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A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If [#permalink]

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23 Sep 2010, 11:45

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A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If the median of these measurements is 6/7 times their arithmetic mean, what is the value of x?

A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If the median of these measurements is 6/7 times their arithmetic mean, what is the value of x?

A. 16 B. 15 C. 14 D. 13 E. 12

{4, 5, 6, 8, 10, x}

Median would be the average of two middle terms --> \(median=\frac{6+8}{2}=7\); \(mean=\frac{4+5+6+8+10+x}{6}=\frac{33+x}{6}\);

A list of measurements in increasing order is 4,5,6,8,10,x. If the med [#permalink]

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20 Jul 2016, 01:21

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A list of measurements in increasing order is 4,5,6,8,10,x. If the median of these measurements is 6/7 times their arithmetic mean, What is the value of x?

Re: A list of measurements in increasing order is 4,5,6,8,10,x. If the med [#permalink]

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20 Jul 2016, 01:49

bimalr9 wrote:

A list of measurements in increasing order is 4,5,6,8,10,x. If the median of these measurements is 6/7 times their arithmetic mean, What is the value of x?

A.16 B.15 C.14 D.13 E.12

This question was locked.

Given a list of measurements in increasing order is 4,5,6,8,10,x and then x is the greatest number in the list.

Median = (6+8)/2 ( since is even number of series)

A list of measurements in increasing order is 4,5,6,8,10,x. If the median of these measurements is 6/7 times their arithmetic mean, What is the value of x?

A.16 B.15 C.14 D.13 E.12

This question was locked.

Merging topics. Please refer to the discussion above.
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A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If [#permalink]

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23 Jul 2016, 00:53

udaymathapati wrote:

A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If the median of these measurements is 6/7 times their arithmetic mean, what is the value of x?

Median of a set with even # of terms = Average of the middle two terms = \(\frac{(6+8)}{2} --->\frac{14}{2} ---> 7\) Median is 7 ; Mean = \(\frac{(4+5+6+8+10+x)}{6}\)

Given that Median = \(\frac{6}{7}\) of Mean

Median =\(\frac{6}{7}* \frac{(4+5+6+8+10+x)}{6}\)

\(7 = \frac{6}{7}* \frac{(4+5+6+8+10+x)}{6}\)

\(7=\frac{6}{7} * \frac{(33+x)}{6}\)

\(49=33+x\)

\(x=49-33\)\(x=16\)

ANSWER IS A
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Re: A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If [#permalink]

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24 Sep 2017, 17:01

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A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If the median of these measurements is 6/7 times their arithmetic mean, what is the value of x?

A. 16 B. 15 C. 14 D. 13 E. 12

We are given the following measurements in increasing order:

4, 5, 6, 8, 10, x

Let’s first calculate the mean:

average = sum/quantity

avg = (4 + 5 + 6 + 8 + 10 + x)/6

avg = (33 + x)/6

We also know that the median of the set is (6 + 8)/2 = 14/2 = 7

Since the the median of these measurements is 6/7 times the arithmetic mean, we can create the following equation:

(6/7)*[(33 + x)/6] = 7

6*(33 + x)/6 = 49

33 + x = 49

x = 16

Answer: A
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