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Math Expert V
Joined: 02 Sep 2009
Posts: 58327
If S = {0, 4, 5, 2, 11, 8}, how much greater than the median  [#permalink]

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If S = {0, 4, 5, 2, 11, 8}, how much greater than the median of the numbers in S is the mean of the numbers in S?

(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
(E) 2.5

Problem Solving
Question: 63
Category: Arithmetic; Algebra Statistics; Concepts of sets
Page: 70
Difficulty: 550

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Math Expert V
Joined: 02 Sep 2009
Posts: 58327
Re: If S = {0, 4, 5, 2, 11, 8}, how much greater than the median  [#permalink]

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SOLUTION

If S = {0, 4, 5, 2, 11, 8}, how much greater than the median of the numbers in S is the mean of the numbers in S?

(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
(E) 2.5

The median of a set with even number of elements is the average of two middle elements, when arranged in ascending/descending order. Thus the median of S = {0, 2, 4, 5, 8, 11} is (4 + 5)/2 = 4.5.

The mean of the set = (0 + 4 + 5 + 2 + 11 + 8)/6 = 5.

The difference = 5 - 4.5 = 0.5.

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Re: If S = {0, 4, 5, 2, 11, 8}, how much greater than the median  [#permalink]

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1
the mean of the numbers is (0+4+5+2+11+8)/6=5
For the median, arrange the numbers in increasing order=0,2,4,5,8,11. The median is therefore (4+5)/2=4.5.

The difference is 0.5.

Senior Manager  Joined: 06 Aug 2011
Posts: 318
Re: If S = {0, 4, 5, 2, 11, 8}, how much greater than the median  [#permalink]

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1
first arrange it in ascending order..... (0,2,4,5,8,11)

4+5/2=4.5 which is median

30/6=5..which is mean...

differnece is .5

A.
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Re: If S = {0, 4, 5, 2, 11, 8}, how much greater than the median  [#permalink]

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1
S={0,2,4,5,8,11}
mEAN = SUMMATION (S) /6 = 30/6 = 5
Median = (4+5) /2 = 4.5

Now the question asks the difference of mean and the median ...therefore, 5-4.5 =0.5

Hence IMO = A
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Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27 Re: If S = {0, 4, 5, 2, 11, 8}, how much greater than the median  [#permalink]

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1
Arrange S in ascending order: {0,2,4,5,8,11}

Since the no. of integers is 6, the median will be determined in this way: (4+5)/2 = 4.5;
Mean = Sum/6 = 30/6 = 5;

Mean - Median = 5 - 4.5 = 0.5;

From this, we can conclude that the Mean is 0.5 higher than the Median value of S.

Ans is (A).
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Re: If S = {0, 4, 5, 2, 11, 8}, how much greater than the median  [#permalink]

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If S = {0, 4, 5, 2, 11, 8}, how much greater than the median of the numbers in S is the mean of the numbers in S?

(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
(E) 2.5

Ordering the given set as S = {0, 2, 4, 5, 8, 11}

$$Median = Average$$ $$of$$ $$middle$$ $$numbers$$ $$= \frac{(4 + 5)}{2} = 4.5$$

$$Mean = \frac{Sum of all elements of S}{Number of elements}= 30/6 = 5$$

So, $$Mean-Median= 5-4.5=0.5$$

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Joined: 12 Sep 2015
Posts: 4000
Re: If S = {0, 4, 5, 2, 11, 8}, how much greater than the median  [#permalink]

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Top Contributor
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If S = {0, 4, 5, 2, 11, 8}, how much greater than the median of the numbers in S is the mean of the numbers in S?

(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
(E) 2.5

To find the median, first arrange the values in ASCENDING ORDER: {0, 2, 4, 5, 8, 11}
Since the set has an EVEN number values, the median will be the average of the two middlemost numbers.
So, median = (4 + 5)/2 = 9/2 = 4.5

Mean = (sum of all values in the set)/(number of values in the set)
= (0 + 4 + 5 + 2 + 11 + 8)/6
= 30/6
= 5

How much greater than the median of the numbers in S is the mean of the numbers in S?
Median = 4.5
Mean = 5

The mean is 0.5 more than the median

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Manager  S
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Re: If S = {0, 4, 5, 2, 11, 8}, how much greater than the median  [#permalink]

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By arranging set S
S = 0,2,4,5,8,11
Median = (5+4)/2 =4.5
Mean = 30/6 = 5
5-4.5 =0.5
So mean is 0.5 greater than median

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Re: If S = {0, 4, 5, 2, 11, 8}, how much greater than the median  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If S = {0, 4, 5, 2, 11, 8}, how much greater than the median of the numbers in S is the mean of the numbers in S?

(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
(E) 2.5

The mean of set S is:

(0 + 4 + 5 + 2 + 11 + 8)/6 = 30/6 = 5

The median is the average of the two middle numbers (when the items in the set are listed in ascending order. Hence, the median is (4 + 5)/2 = 4.5

So the mean is 5 - 4.5 = 0.5 greater than the median.

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Intern  B
Joined: 16 Jun 2015
Posts: 1
Re: If S = {0, 4, 5, 2, 11, 8}, how much greater than the median  [#permalink]

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why can't we calculate mean as 11-0/2? which is 5.5 Re: If S = {0, 4, 5, 2, 11, 8}, how much greater than the median   [#permalink] 15 Dec 2018, 06:42
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