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Math Expert V
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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1 00:00

Difficulty:   15% (low)

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

### HideShow timer Statistics 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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Posts: 3359
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Re: What is the difference between the mean and the median of the positive  [#permalink]

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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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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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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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Senior Manager  P
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GMAT 1: 560 Q42 V25 GMAT 2: 570 Q43 V27 GMAT 3: 710 Q49 V39 Re: What is the difference between the mean and the median of the positive  [#permalink]

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Mean = Median = k+6

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

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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

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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GMAT 1: 700 Q43 V42 Re: What is the difference between the mean and the median of the positive  [#permalink]

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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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Joined: 27 Nov 2018
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GMAT 1: 510 Q33 V28 Re: What is the difference between the mean and the median of the positive  [#permalink]

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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
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1234
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: What is the difference between the mean and the median of the positive  [#permalink]

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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

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