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If the variables, X, Y, and Z take on only the values 10, 20

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If the variables, X, Y, and Z take on only the values 10, 20  [#permalink]

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New post 11 Mar 2014, 02:07
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Image
If the variables, X, Y, and Z take on only the values 10, 20, 30, 40, 50, 60, or 70 with frequencies indicated by the shaded regions above, for which of the frequency distributions is the mean equal to the median?

(A) X only
(B) Y only
(C) Z only
(D) X and Y
(E) X and Z

Problem Solving
Question: 148
Category: Arithmetic Statistics
Page: 81
Difficulty: 650


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Re: If the variables, X, Y, and Z take on only the values 10, 20  [#permalink]

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New post 11 Mar 2014, 02:08
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SOLUTION

Image
If the variables, X, Y, and Z take on only the values 10, 20, 30, 40, 50, 60, or 70 with frequencies indicated by the shaded regions above, for which of the frequency distributions is the mean equal to the median?

(A) X only
(B) Y only
(C) Z only
(D) X and Y
(E) X and Z

The frequency distributions for both X and Z are symmetric about 40, which means that both X and Z have mean = median = 40.

Answer: E.
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Re: If the variables, X, Y, and Z take on only the values 10, 20  [#permalink]

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New post 11 Mar 2014, 07:19
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For Mean and Median to be same, the data should be evenly distributed around the mean. Also, if the distribution is symmetrical, the mean is equal to median.

In X and Z, we can conclude that the mean and median is same because the distribution is symmetrical around the mean (40).

In Y, however, median will be a clearly be multiple of 10 but the mean comes out to be 760/18 which is not a multiple of 10. So clearly Y is not an option to pick.

Therefore, IMO, answer is E.
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Re: If the variables, X, Y, and Z take on only the values 10, 20  [#permalink]

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New post 11 Mar 2014, 02:26
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Attachment:
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If the variables, X, Y, and Z take on only the values 10, 20, 30, 40, 50, 60, or 70 with frequencies indicated by the shaded regions above, for which of the frequency distributions is the mean equal to the median?

(A) X only
(B) Y only
(C) Z only
(D) X and Y
(E) X and Z

Sol: Ans is E

Consider data for Variable X

We see that it is symmetric about 40 and hence the distribution is equally spaced and therefore Mean =Median
We can also spread the distribution as
10,20,20,30,30,30,40,40,40,40,50,50,50,60,60,70.. Strike out from extremes and we get Median= 40
And the Mean will be (40*4+10*1+20*2+30*3+50*3+60*2+70*1)/16 or 640/16= 40

Similar symmetry can be observed for Z distribution as well.
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Re: If the variables, X, Y, and Z take on only the values 10, 20  [#permalink]

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New post 11 Mar 2014, 06:49
Isnt it too dificult to culculate !

I was going for x only.. bt looking at the z ..it seems it will have same median and mean..what is easiest way to solve
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Re: If the variables, X, Y, and Z take on only the values 10, 20  [#permalink]

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New post 11 Mar 2014, 08:01
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When the distribution is symmetric, mean equals median. Thus, X and Z must be in the answer. There is no choice with X, Y, and Z, so there is no need to check Y. The answer is E.
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Re: If the variables, X, Y, and Z take on only the values 10, 20  [#permalink]

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New post 11 Mar 2014, 08:28
For X: The distribution is symmetric and more populated at mean. So for this mean = median
For Y: The distribution is neither symmetric nor populated at mean. So for this mean is not equal to median
For Z: The distribution is symmetric but more populated at ends. So mean is shifted towards right side. Thus mean is not equal to median.

Answer: A
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Re: If the variables, X, Y, and Z take on only the values 10, 20  [#permalink]

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New post 11 Mar 2014, 19:02
Answer = (E) X and Z

Looking at the charts, see that X & Z are symmetric.

So, Answer = E
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Re: If the variables, X, Y, and Z take on only the values 10, 20  [#permalink]

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New post 10 Apr 2016, 03:08
As per the 3 figures given in the question , it can be clearly seen that for graphs X and Z mean is equal to median
correct answer - E
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Re: If the variables, X, Y, and Z take on only the values 10, 20  [#permalink]

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New post 22 Mar 2017, 14:52
try to estimate, this is what worked for me:
both X and Z looks similar and approx. gets us to the same mean and median
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Re: If the variables, X, Y, and Z take on only the values 10, 20  [#permalink]

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New post 27 May 2018, 01:53
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Bunuel, VeritasPrepKarishma, EgmatQuantExpert please share the theory of these types of problem.
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Re: If the variables, X, Y, and Z take on only the values 10, 20  [#permalink]

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New post 28 May 2018, 04:31
sadikabid27 wrote:
Bunuel, VeritasPrepKarishma, EgmatQuantExpert please share the theory of these types of problem.


The theory of this question is the same as the theory of mean and median. It uses no new concepts. In both X and Z, the numbers are symmetrical about the centre. So the sum of the deviation of numbers on the left of the centre is same as the sum of the deviation of the numbers on the right.
This post explains finding mean using deviations: https://www.veritasprep.com/blog/2012/0 ... eviations/

If the set of numbers is 10, 15, 15, 20, 25, 25, 30, the mean will simply be 20. Notice the symmetry around the centre, 20. The median will obviously be 20 too.

The case with X and Z is exactly the same.

Y has a random sequence. There is no symmetry about the centre and hence the mean will not be the same as the median.
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Re: If the variables, X, Y, and Z take on only the values 10, 20  [#permalink]

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New post 24 Jun 2018, 23:33
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Bunuel can I say, that in an evenly distributed set, the mean = median. and thus "E" is the right answer here ?

I used this logic to answer
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Re: If the variables, X, Y, and Z take on only the values 10, 20 &nbs [#permalink] 24 Jun 2018, 23:33
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