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contact.sumeshn
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Post subject: Statistics  Posted: Fri Jul 09, 2010 3:08 am |
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Posts: 12
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Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?
A. 78
B. 77 1/5
C. 66 1/7
D. 55 1/7
E. 52
given that mean = median, should we also consider the fact that set R is an evenly spaced set? Or is it true that whenever a set has the same mean and median, the set is an equally spaced set?
Thanks!
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kalyan_tcs08
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Post subject: Re: Statistics Posted: Sat Jul 10, 2010 1:32 pm |
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Posts: 2
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contact.sumeshn wrote: Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?
A. 78
B. 77 1/5
C. 66 1/7
D. 55 1/7
E. 52
given that mean = median, should we also consider the fact that set R is an evenly spaced set? Or is it true that whenever a set has the same mean and median, the set is an equally spaced set?
Thanks! You need not worry about mean and median while considering this problem... say the numbers in set R as a, b, c, d, e. a+b+c+d+e = 5*55= 275 since mean = median=55, a+b+55+d+e = 275 a+b+d+(3a+20) = 220 4a+b+d = 200 Now do some thinking,, if the range needs to be maximum...the end numbers a, e must be as far as possible from each other. so the numbers b ,d should be as minimum as possible. b is nearer to a , so it can take a min value of A. similarly, d is nearer to c so can take value of C. so the equation becomes, 4a + (a) + 55 = 220 5a = 145 ; a=29, e= 107 range = 78 cheers!!!
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debmalya.dutta
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Post subject: Re: Statistics Posted: Sun Jul 11, 2010 11:23 am |
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Posts: 47
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R need not be an event spaced set for example 53,54,55,56,57 vs say 50,54,55,56,60 contact.sumeshn wrote: Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?
A. 78
B. 77 1/5
C. 66 1/7
D. 55 1/7
E. 52
given that mean = median, should we also consider the fact that set R is an evenly spaced set? Or is it true that whenever a set has the same mean and median, the set is an equally spaced set?
Thanks!
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mschwrtz
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Post subject: Re: Statistics Posted: Mon Jul 12, 2010 10:32 pm |
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Posts: 506
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that's right debmalya.dutta.
evenly distributed values-->(mean=median)
BUT
(mean=median)-/->evenly distributed values.
if you take the difference between each number less than the mean and the mean itself and add all those differences together, the sum will be exactly the same as if you take the difference between each number greater than the mean and the mean itself and add all those differences together.
Huh? Well consider debmalya.dutta's example, 50,54,55,56,60. The mean is 55. (55-50)+(55-54)=(56-55)+(60-55).
This implies that median=mean for every set of evenly distributed values, and also for every set of values distributed symmetrically about the mean (in this case, 5 less, 1 less, mean, 1 more, 5 more.. We could generate other, even less obvious cases too, where there's no evident symmetry, e.g. 50, 52, 53, 55, 56, 59, 60.
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debmalya.dutta
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Post subject: Re: Statistics Posted: Tue Jul 13, 2010 10:31 pm |
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Posts: 47
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Quoting Tim Sanders's(MGMAT staff) explanation on this from a different post
If you want to maximize the highest element in a set of fixed sum, you need to make the other elements as small as possible. If we have a, _, 55, _, max in ascending order, you need to push each of the blanks as low as possible. This can be done by making the first blank a and the second one 55..
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mschwrtz
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Post subject: Re: Statistics Posted: Sun Aug 22, 2010 11:58 am |
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| ManhattanGMAT Staff |
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Posts: 506
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Thanks debmalya.dutta, that's correct. I only spoke to the narrow point about evenly distributed values.
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