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

Question

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

pushpitkc · Answer

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)

GMATBusters · Answer

As for equally spaced data, median = mean.

Their difference = 0.

Answer = A

Posted from my mobile device

GMATinsight · Answer

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

Answer: option A

US09 · Answer

Mean = Median = k+6

Hence, A.

ScottTargetTestPrep · Answer

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.

Answer: A

ramblers · Answer

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

Answer A

pandajee · Answer

Hi  gmatbusters

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

GMATBusters · Answer

You are right, 
The terms are not equally spaced. It was an error on my part.

MHIKER · Answer

I plugged  1  for  k,

The mean  = \frac{1+4+5+9+10+13}{6}=\frac{42}{6}=7

The median = \frac{5+9}{2}=7

The difference  = 7-7=0

The answer is  A

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

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

Prep Toolkit

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