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Is the median of class A and class B combined greater than the mean of

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Is the median of class A and class B combined greater than the mean of  [#permalink]

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New post Updated on: 29 Mar 2019, 06:35
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Is the median of class A and class B combined greater than the mean of class A and class B combined?

(1) a + b = 69
(2) a = 37, b = 32

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Originally posted by EncounterGMAT on 06 Dec 2018, 09:56.
Last edited by Bunuel on 29 Mar 2019, 06:35, edited 3 times in total.
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Re: Is the median of class A and class B combined greater than the mean of  [#permalink]

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New post Updated on: 23 Dec 2018, 00:36
topper97 wrote:
Is the median of class A and class B combined greater than the mean of class A and class B combined?

(1) a+b=69
(2) a=37, b=32

can someone explain this question? Thanks!


Basics: By definition, to find median of a given set of numbers, all numbers need to be arranged in ascending/descending order, and then pick the middle number.

Statement 1: a+b=69. Mean = \(\frac{(72a + 69b)}{a+b}\)
Mean cannot be found as we do not know 'a' and 'b'. Median cannot be found as we do not know values of set 'a' and set 'b'
Insufficient

Statement 2: a=37, b = 32
Mean can be found since we have 'a' and 'b'. However, median cannot be found as we do not know values of set 'a' and set 'b'.
Insufficient

Statement 1 & 2:
To find combined median of the 2 sets, we will have to combine all numbers of both sets and pick the middle value. We do not have all values of both sets.
Insufficient

Hence, E

Must confess that I marked the answer D because I thought Median of 2 sets = \(\frac{Median(set A) + Median(set B)}{MedianA+ MedianB}\)
However, that is an incorrect approach.
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Originally posted by Darshi04 on 22 Dec 2018, 14:13.
Last edited by Darshi04 on 23 Dec 2018, 00:36, edited 1 time in total.
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Re: Is the median of class A and class B combined greater than the mean of  [#permalink]

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New post 22 Dec 2018, 17:37
Darshi04 wrote:
topper97 wrote:
Is the median of class A and class B combined greater than the mean of class A and class B combined?

(1) a+b=69
(2) a=37, b=32

can someone explain this question? Thanks!


Basics: By definition, to find median of a given set of numbers, all numbers need to be arranged in ascending/descending order, and then pick the middle number.

Statement 1: a+b=69. By knowing the total number of students in the class, we can find mean, i.e \(\frac{Mean(a) + Mean(a)}{a + b}\)
However, median cannot be found as we do not know values of set 'a' and set 'b'
Insufficient

Statement 2: a=37, b = 32
Median cannot be found as we do not know values of set 'a' and set 'b'.
Insufficient

Statement 1 & 2:
To find combined median of the 2 sets, we will have to combine all numbers of both sets and pick the middle value. We do not have all values of both sets.
Insufficient

Hence, E

Must confess that I marked the answer D because I thought Median of 2 sets = \(\frac{Median(set A) + Median(set B)}{MedianA+ MedianB}\)
However I believe this can be done only in case of Mean.


I think there should be a correction in your explanation for St 1

Mean for both the classes combined = \(\frac{(72a + 69b)}{( a +b )}\)

= \(\frac{(72a + 69b)}{(69)}\)

Cannot be found
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Re: Is the median of class A and class B combined greater than the mean of  [#permalink]

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New post 23 Dec 2018, 00:31
ksrutisagar wrote:
Darshi04 wrote:
topper97 wrote:
Is the median of class A and class B combined greater than the mean of class A and class B combined?

(1) a+b=69
(2) a=37, b=32

can someone explain this question? Thanks!


Basics: By definition, to find median of a given set of numbers, all numbers need to be arranged in ascending/descending order, and then pick the middle number.

Statement 1: a+b=69. By knowing the total number of students in the class, we can find mean, i.e \(\frac{Mean(a) + Mean(a)}{a + b}\)
However, median cannot be found as we do not know values of set 'a' and set 'b'
Insufficient

Statement 2: a=37, b = 32
Median cannot be found as we do not know values of set 'a' and set 'b'.
Insufficient

Statement 1 & 2:
To find combined median of the 2 sets, we will have to combine all numbers of both sets and pick the middle value. We do not have all values of both sets.
Insufficient

Hence, E

Must confess that I marked the answer D because I thought Median of 2 sets = \(\frac{Median(set A) + Median(set B)}{MedianA+ MedianB}\)
However I believe this can be done only in case of Mean.


I think there should be a correction in your explanation for St 1

Mean for both the classes combined = \(\frac{(72a + 69b)}{( a +b )}\)

= \(\frac{(72a + 69b)}{(69)}\)

Cannot be found


ksrutisagar
Ahh, thanks for pointing that out. Will edit the response!
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Re: Is the median of class A and class B combined greater than the mean of   [#permalink] 23 Dec 2018, 00:31
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