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# Class A and B took a same test. For class A, median score is

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Manager
Joined: 28 Mar 2006
Posts: 145
Class A and B took a same test. For class A, median score is  [#permalink]

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19 May 2006, 06:42
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21. Class A and B took a same test. For class A, median score is 80, average score is 82; for class B, median score is 78, average score is 74. Combining A and B, is the average greater than the median?

1). A has 37 students and B has 40 students.

2). A and B have 77 students.

how will we find the median of A n B combined.?

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Director
Joined: 16 Aug 2005
Posts: 914
Location: France

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19 May 2006, 07:23
(1)
Class A: 37 students.
Median = 80 = score of 19th student. Meaning 18 students scored below 80 and 18 students scored above 80.
Average = 82 = score of all students/37

Class B: 40 students.
Median = 78 = average of 20st and 21nd student
Average = 74 = total score of class/40

Combining both, average = (82*37 + 74*40) / 77 = 77.85 = 78
Not sure how to find median, so I would say not sufficient.

(2) Combined average = 78
Median store < 80 and >78

So Sufficient.

B...
Manager
Joined: 28 Mar 2006
Posts: 145

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19 May 2006, 07:31
The info given in stmt B is also presnt in stmt A.
A says A has 37 students n B has 40 students.i.e An B combned have 77 studnts......stmt B only tells the total...
Also, using A...only can we calculate the average score of entire class.
hever m not sure hw to find the median of the combined class.

gmatmba wrote:
(1)
Class A: 37 students.
Median = 80 = score of 19th student. Meaning 18 students scored below 80 and 18 students scored above 80.
Average = 82 = score of all students/37

Class B: 40 students.
Median = 78 = average of 20st and 21nd student
Average = 74 = total score of class/40

Combining both, average = (82*37 + 74*40) / 77 = 77.85 = 78
Not sure how to find median, so I would say not sufficient.

(2) Combined average = 78
Median store < 80 and >78

So Sufficient.

B...
Manager
Joined: 23 Jan 2006
Posts: 191

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19 May 2006, 07:38
1
itishaj wrote:
21. Class A and B took a same test. For class A, median score is 80, average score is 82; for class B, median score is 78, average score is 74. Combining A and B, is the average greater than the median?

1). A has 37 students and B has 40 students.

2). A and B have 77 students.

how will we find the median of A n B combined.?

class A: there are 18 students below 80 and 18 students above 80
class B: there are 20 students below 78 and 20 students above 78.
(1) the average of all students is (37*82 + 40*74)/77 ~= 77.8
you know that in the total, you have 38 students that are above 78, so the median is below 78.
SUFFICIENT

(2) we cannot determine the mean for both grades without knowing the weight of the two medians of each grade.

A it is.
Manager
Joined: 10 May 2006
Posts: 183
Location: USA

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19 May 2006, 13:20
kook44 wrote:
itishaj wrote:
21. Class A and B took a same test. For class A, median score is 80, average score is 82; for class B, median score is 78, average score is 74. Combining A and B, is the average greater than the median?

1). A has 37 students and B has 40 students.

2). A and B have 77 students.

how will we find the median of A n B combined.?

class A: there are 18 students below 80 and 18 students above 80
class B: there are 20 students below 78 and 20 students above 78.
(1) the average of all students is (37*82 + 40*74)/77 ~= 77.8
you know that in the total, you have 38 students that are above 78, so the median is below 78.
SUFFICIENT

(2) we cannot determine the mean for both grades without knowing the weight of the two medians of each grade.

A it is.

Great explanation Kook44. I was also stuck on how to find the median until I read your answer.
Intern
Joined: 04 May 2006
Posts: 49

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19 May 2006, 22:20
Quote:
class A: there are 18 students below 80 and 18 students above 80
class B: there are 20 students below 78 and 20 students above 78.
(1) the average of all students is (37*82 + 40*74)/77 ~= 77.8
you know that in the total, you have 38 students that are above 78, so the median is below 78.
SUFFICIENT

(2) we cannot determine the mean for both grades without knowing the weight of the two medians of each grade.

A it is.

class B: there are 20 students below 78 and 20 students above 78.
In Class B, Median is 78 of 40 students. So we can say that there are 18 students more than 78 marks and 18 less than 78. for middle two students,Average is 78 (median), so 1 can be less than 78 and other can be more than 78 or both can be 78. So for sure, we can say that there are 19(Class B)+18(Class A) = 37 students equal or greater than 78.
Now, there are total 77 students and for median we need to know the marks of 39th student, that can't be deduced from here.
So I think Answer is E.
_________________

If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut.
Albert Einstein

Manager
Joined: 28 Mar 2006
Posts: 145

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20 May 2006, 02:01
kook44 wrote:
itishaj wrote:
21. Class A and B took a same test. For class A, median score is 80, average score is 82; for class B, median score is 78, average score is 74. Combining A and B, is the average greater than the median?

1). A has 37 students and B has 40 students.

2). A and B have 77 students.

how will we find the median of A n B combined.?

class A: there are 18 students below 80 and 18 students above 80
class B: there are 20 students below 78 and 20 students above 78.
(1) the average of all students is (37*82 + 40*74)/77 ~= 77.8
you know that in the total, you have 38 students that are above 78, so the median is below 78.SUFFICIENT

(2) we cannot determine the mean for both grades without knowing the weight of the two medians of each grade.

A it is.

Hi kook..hw did u conclude that median is below 78, given that 38students hav > 78 marks. I didnt get it..plz explain in brief.

Thanks
Itisha
Senior Manager
Joined: 09 Mar 2006
Posts: 424

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20 May 2006, 04:12
A) The average of the A&B combined is ~77.8, which is smaller then
the smalest medium of two classes . Since in combined class the medium
will never be smaller then the smalest medium of two separated classes, A is sufficient.

B) Since we don't know the ratio of students distribution between two classes , B is insufficient.

A it is
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Posts: 9457
Re: Class A and B took a same test. For class A, median score is  [#permalink]

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03 Jan 2018, 15:53
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Re: Class A and B took a same test. For class A, median score is &nbs [#permalink] 03 Jan 2018, 15:53
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