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The scores on a certain history test are shown above. How

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The scores on a certain history test are shown above. How [#permalink] New post 10 Apr 2013, 00:21
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Question Stats:

72% (01:38) correct 28% (01:07) wrong based on 58 sessions
40, 45, 45, 50, 50, 60, 70, 75, 95, 100

The scores on a certain history test are shown above. How many scores were greater than the median score but less than the mean score?

A. None
B. One
C. Two
D. Three
E. Four
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Apr 2013, 00:25, edited 1 time in total.
Renamed the topic and edited the tags.
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Re: The scores on a certain history test are shown above. How [#permalink] New post 10 Apr 2013, 00:33
Expert's post
score780 wrote:
40, 45, 45, 50, 50, 60, 70, 75, 95, 100

The scores on a certain history test are shown above. How many scores were greater than the median score but less than the mean score?

A. None
B. One
C. Two
D. Three
E. Four


The median = (the average of two middle terms) = (50 + 60)/2 = 55.
The mean = (the sum)/(# of terms) = 630/10 = 63.

Only 60 is between 55 and 63.

Answer: B.
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Re: The scores on a certain history test are shown above. How [#permalink] New post 10 Apr 2013, 00:37
Bunuel wrote:
score780 wrote:
40, 45, 45, 50, 50, 60, 70, 75, 95, 100

The scores on a certain history test are shown above. How many scores were greater than the median score but less than the mean score?

A. None
B. One
C. Two
D. Three
E. Four


The median = (the average of two middle terms) = (50 + 60)/2 = 55.
The mean = (the sum)/(# of terms) = 630/10 = 63.

Only 60 is between 55 and 63.

Answer: B.


Thanks, yes this is the classic way. Is there a shortcut especially for calculating the mean without having to really do it?
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Re: The scores on a certain history test are shown above. How [#permalink] New post 10 Apr 2013, 01:40
Thanks, yes this is the classic way. Is there a shortcut especially for calculating the mean without having to really do it?[/quote]


In this problem , yes you can calculate it in 10 seconds , if you can observe the total number of terms is 10. so since every number is a multiple of 10 you can do it easily .

If there is a general method do let me know.
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Re: The scores on a certain history test are shown above. How [#permalink] New post 10 Apr 2013, 01:46
venkat18290 wrote:
Thanks, yes this is the classic way. Is there a shortcut especially for calculating the mean without having to really do it?



In this problem , yes you can calculate it in 10 seconds , if you can observe the total number of terms is 10. so since every number is a multiple of 10 you can do it easily .

If there is a general method do let me know.[/quote]

Ok got it, thanks
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Re: The scores on a certain history test are shown above. How [#permalink] New post 11 Apr 2013, 07:03
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score780 wrote:

Thanks, yes this is the classic way. Is there a shortcut especially for calculating the mean without having to really do it?


40, 45, 45, 50, 50, 60, 70, 75, 95, 100

You can use deviations to find the mean here.

Assume that the mean is 60 since it's kind of in the middle.

Now notice that 50 is 10 less than 60 and 70 is 10 more so ignore both.
Now 40, 45, 45, 50 together are 60 away from 60 while 75, 95, 100 are 90 away from 60.

So we have a total of 90 - 60 = 30 deviation from 60. Since there are 10 numbers, the average must be 30/10 = 3 more than 60 i.e it must be 63.

Check this for more on this method:
http://www.veritasprep.com/blog/2012/05 ... eviations/

For a general discussion on mean, see
http://www.veritasprep.com/blog/2012/04 ... etic-mean/
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Re: The scores on a certain history test are shown above. How   [#permalink] 11 Apr 2013, 07:03
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