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# One class has 25 students, they take a test, is the median

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CEO
Joined: 15 Aug 2003
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One class has 25 students, they take a test, is the median [#permalink]  14 Sep 2003, 05:33
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One class has 25 students, they take a test, is the median
greater than their mean?

A All of them score between 70 and 100.
B More than half score more than 85.

Is it E?

Intern
Joined: 06 Sep 2003
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Location: island
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B?

More than half score more than 85, so median is more than 85.

If the remain ones score are all 84, we may got the mean to be 84.52.

[(85*13)+(84*12)]/25=84.52<85
Intern
Joined: 28 Aug 2003
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Location: USA
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mystery wrote:
B?

More than half score more than 85, so median is more than 85.

If the remain ones score are all 84, we may got the mean to be 84.52.

[(85*13)+(84*12)]/25=84.52<85

I think it is E.

Statement I - Insufficient

Explanation: Several possibilities here. Imagine all numbers to be 71. So, median would be 71 and mean would be 70.xx. In this case, mean < median. However, imagine 13 students got 71 and rest (12) students got 99. Then, median is still 71. And mean is 75.xx. In this case mean > median.

Statement II - Insufficient

Explanation: Imagine 12 students got 71. And rest (13) got 86. Then, median is 86 and mean is 78.xx. So, mean < median in this case. Consider case (ii) under statement I above which proves mean > median.

Hope my answer is correct and that I didn't confuse you too much. If anyone doesn't agree with my explanation, please let me know.

Thanks.
Intern
Joined: 17 Sep 2003
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"Consider case (ii) under statement I above which proves mean > median. "

In case (ii) under statement I, more than half the number of students did not score more than 85, (u have assumed 13 scored 71) so mean > median proves wrong.

So I agree with the answer B.
Manager
Joined: 28 Feb 2003
Posts: 147
Location: Kiev
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Kudos [?]: 4 [0], given: 0

Could somebody give definitions of "mean" and "median"?
I met these terms before but they still confuse me
_________________

Too much is not enough...

Intern
Joined: 27 May 2003
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Just wondering what will happen when all score 85?
Senior Manager
Joined: 11 Nov 2003
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Location: Illinois
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I get E.

Statement - I : NOT SUFFECIENT. We do not have mnuch information

Statement II: NOT SUFFECIENT

case-1, 12 students get 85, 13 students get 86. So median is 86, but the mean is surely less than 86, so mean < median, ANSWER NO

case-2: 12 students get 85, 1 student get 86, the remaining 12 students get 100. So median is still 86, but the mean has shifted above 86. So mean > median. ANSWER IS YES.

BOTH COMBINED:

not suffecient, the above explanation is enough.

GMAT Club Legend
Joined: 07 Jul 2004
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I feel it's E. Both statements, used alone or together , can't tell you for sure which is the greater.

Generally, I freak out a little whenever I see a median or standard deviation questions... hope I don't see much of those on test day !
Senior Manager
Joined: 25 Jul 2004
Posts: 274
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Kudos [?]: 7 [0], given: 0

Defintely E.

Taking both statements together, I could restrict all the test scores in the range from

86 to 100

and still come out with cases when the median is less than and greater than the mean.
Senior Manager
Joined: 22 Jun 2004
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Location: Bangalore, India
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Mean is nothing but the average i.e., sum of all the numbers/number of numbers

Median is the middle number when arranged in acending or descending order. It is unique if the number of numbers arranged is odd. Otherwise(when the number of numbers are even and are arranged in ascending/descending order), the two middle numbers are averaged to get the median i.e., (a+b/2)

Mode is the most frequently recurring number/numbers among the given set of numbers. It can be more than one.

bono wrote:
Could somebody give definitions of "mean" and "median"?
I met these terms before but they still confuse me

_________________

Awaiting response,

Thnx & Rgds,
Chandra

Director
Joined: 14 Jul 2004
Posts: 700
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Kudos [?]: 11 [0], given: 0

Prae: What is the OA? I got to answer choice "E"......Gmatblast does a good job of explaining why E is the answer.
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