The variables A, B, and C have values o : GMAT Problem Solving (PS)
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# The variables A, B, and C have values o

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The variables A, B, and C have values o [#permalink]

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07 Jan 2013, 10:01
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The variables A, B, and C have values of 15, 20, 25, 30, 35, 40, and 45 with frequencies as indicated by the graphs below. For which of these frequency distributions is the median equal to the mean?
A. A only
B. B only
C. C only
D. A and B only
E. A, B, and C

Based on previous questions, I know that the answer is D. However, how could I know that graph C should not be chosen without making calculations?
Could I answer this questions just seeing the graphs? How? Thanks!

Source: http://www.grockit.com
[Reveal] Spoiler: OA

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Re: The variables A, B, and C have values o [#permalink]

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07 Jan 2013, 10:25
IMO, there is no way you can see the graph of C and judge. You need to calculate for C. For A and B though symmetry should be enough.
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Re: The variables A, B, and C have values o [#permalink]

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07 Jan 2013, 10:37
the y-axis is the # of times the frequency is included in the distribution. For the first two graphs the pattern is uniform (4,3,2,1,2,3,4) and (1,2,3,4,3,2,1). This means the mean = median.

The 3rd graph is scattered (3,3,1,2,4,1,1) and the # of frequencies are not uniform. Therefore mean cannot equal median.
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Re: The variables A, B, and C have values o [#permalink]

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08 Jan 2013, 01:55
danzig wrote:
The variables A, B, and C have values of 15, 20, 25, 30, 35, 40, and 45 with frequencies as indicated by the graphs below. For which of these frequency distributions is the median equal to the mean?
A. A only
B. B only
C. C only
D. A and B only
E. A, B, and C

Based on previous questions, I know that the answer is D. However, how could I know that graph C should not be chosen without making calculations?
Could I answer this questions just seeing the graphs? How? Thanks!

Source: http://www.grockit.com

Hi,

I think you are convinced about the graphs for A & B. But you wish to know approach on how to disqualify graph C. Right!

Let's look at the frequency distribution of graph A & B.

For A

Values Frequencies
--15----------4------
--20----------3------
--25----------2------
--30----------1------
--35----------2------
--40----------3------
--45----------4------

It is quite evident that frequency distribution follows homogeneity. So For graph A, mean & median would be equal.

Now, we see graph B.

For B

Values Frequencies
--15----------1------
--20----------2------
--25----------3------
--30----------4------
--35----------3------
--40----------2------
--45----------1------

It is quite evident that frequency distribution follows homogeneity. So For graph B too, mean & median would be equal.

Now, we see graph C.

For C

Values Frequencies
--15----------3------
--20----------3------
--25----------1------
--30----------2------
--35----------4------
--40----------1------
--45----------1------

It is quite evident that frequency distribution follows heterogeneity. So for graph C, mean & median would be not be equal.

Hope this is clear to you now.

-Shalabh Jain
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Re: The variables A, B, and C have values o   [#permalink] 08 Jan 2013, 01:55
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