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# What is the difference between the mean and the median of the positive

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Math Expert
Joined: 02 Sep 2009
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What is the difference between the mean and the median of the positive  [#permalink]

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29 Mar 2018, 00:24
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Difficulty:

15% (low)

Question Stats:

91% (01:10) correct 9% (01:37) wrong based on 47 sessions

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What is the difference between the mean and the median of the positive numbers, k, k + 3, k + 4, k + 8, k + 9, k + 12?

(A) 0
(B) 1
(C) 6
(D) 2k
(E) 5k

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Re: What is the difference between the mean and the median of the positive  [#permalink]

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29 Mar 2018, 01:27
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Bunuel wrote:
What is the difference between the mean and the median of the positive numbers, k, k + 3, k + 4, k + 8, k + 9, k + 12?

(A) 0
(B) 1
(C) 6
(D) 2k
(E) 5k

In a set of 6 elements, the median is the average of the middle two terms.

The median of the 6 elements is $$\frac{k+4+k+8}{2} = k+6$$

The mean of the 6 elements is $$\frac{6k + (3+4+8+9+12)}{6} = \frac{6k + 36}{6} = k + 6$$

Therefore, the difference between mean and median is 0(Option A)
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Re: What is the difference between the mean and the median of the positive  [#permalink]

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29 Mar 2018, 02:55
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As for equally spaced data, median = mean.

Their difference = 0.

Posted from my mobile device
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What is the difference between the mean and the median of the positive  [#permalink]

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29 Mar 2018, 04:11
Bunuel wrote:
What is the difference between the mean and the median of the positive numbers, k, k + 3, k + 4, k + 8, k + 9, k + 12?

(A) 0
(B) 1
(C) 6
(D) 2k
(E) 5k

GMAT INSIGHT:

Mean - Sum of the numbers in the sets / Number of terms in the Set

Median - Middle term (If the number of terms in the set is ODD) OR Average of two middle terms (If the number of terms in the set is EVEN) After arranging the term in Increasing/Decreasing order

Mean = Sum of (k, k + 3, k + 4, k + 8, k + 9, k + 12) / 6 = 6k+36 / 6 = k+6

Median = Average of ( k + 4 and k + 8) = 2k+12 / 2 = k+6

Mean - Median = (k+6) - (k+6) = 0

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Re: What is the difference between the mean and the median of the positive  [#permalink]

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29 Mar 2018, 14:30
Mean = Median = k+6

Hence, A.
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Re: What is the difference between the mean and the median of the positive  [#permalink]

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30 Mar 2018, 10:50
Bunuel wrote:
What is the difference between the mean and the median of the positive numbers, k, k + 3, k + 4, k + 8, k + 9, k + 12?

(A) 0
(B) 1
(C) 6
(D) 2k
(E) 5k

The mean is:

(6k + 3 + 4 + 8 + 9 + 12)/6 = (6k + 36)/6 = k + 6

The median is:

(k + 4 + k + 8)/2 = (2k + 12)/2 = k + 6

So the difference is zero.

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Re: What is the difference between the mean and the median of the positive  [#permalink]

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30 Mar 2018, 17:32
As an alternative way of solving this, you can plug in k = 1 to solve for the median and mean. Doing so gives you the set {1, 4, 5, 9, 10, 13}

Median = (5 + 9) / 2 = 7
Mean = (1 + 4 + 5 + 9 + 10 + 13) / 6 = 7

7 - 7 = 0

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Re: What is the difference between the mean and the median of the positive  [#permalink]

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08 May 2019, 10:39
gmatbusters wrote:
As for equally spaced data, median = mean.

Their difference = 0.

Posted from my mobile device

Hi gmatbusters

How come here the terms are equally spaced ?
k, k + 3, k + 4, k + 8, k + 9, k + 12
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Re: What is the difference between the mean and the median of the positive  [#permalink]

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08 May 2019, 19:05
You are right,
The terms are not equally spaced. It was an error on my part.
pandajee wrote:
gmatbusters wrote:
As for equally spaced data, median = mean.

Their difference = 0.

Posted from my mobile device

Hi gmatbusters

How come here the terms are equally spaced ?
k, k + 3, k + 4, k + 8, k + 9, k + 12

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Re: What is the difference between the mean and the median of the positive   [#permalink] 08 May 2019, 19:05
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