The variables A, B, and C have values of 15, 20, 25, 30, 35, 40, and

Question

https://gmatclub.com/forum/download/file.php?id=19164 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 Median - media.png 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: https://www.grockit.com

AbhiJ · Answer

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.

sambam · Answer

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.

egmat · Answer

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

bumpbot · Answer

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The variables A, B, and C have values of 15, 20, 25, 30, 35, 40, and

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The variables A, B, and C have values of 15, 20, 25, 30, 35, 40, and

Prep Toolkit

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