Mean Vs Median

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Wed Jan 04, 2012 9:44 pm

Set T contains more than one element. Is the median of set T greater than its mean?
(1) Set S has positive range.
(2) The elements of the set are not consecutive integers

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Source: Beat The GMAT — Data Sufficiency | Wed Jan 04, 2012 9:44 pm

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Wed Jan 04, 2012 9:59 pm

karthikpandian19 wrote:Set T contains more than one element. Is the median of set T greater than its mean?
(1) Set S has positive range.
(2) The elements of the set are not consecutive integers

(1) Set S has positive range.
Clearly insufficient

(2) The elements of the set are not consecutive integers
Mean and median for {2,4,6,8,10} are the same
Mean and media for {1.7.10.103} are not the same
insufficient

Combining two statements
Still insufficient

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Thu Jan 05, 2012 9:07 pm

OA is E

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Fri Jan 06, 2012 5:44 am

karthikpandian19 wrote:Set T contains more than one element. Is the median of set T greater than its mean?
(1) Set S has positive range.
(2) The elements of the set are not consecutive integers

(1) Set T has a positive range means T can have any range of numbers from 1 till infinity; NOT sufficient.

(2) The elements of the set are not consecutive integers implies it could be any range of numbers from 1 till infinity; NOT sufficient.

Combining (1) and (2), again is NOT sufficient to find if the median of set T is greater than its mean.

The correct answer is E.

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ArunangsuSahu: Master | Next Rank: 500 Posts; Posts: 382; Joined: Thu Mar 31, 2011 5:47 pm; Thanked: 15 times

by ArunangsuSahu » Fri Jan 06, 2012 8:40 am

Let's give a simpler explanation

Remember 1 thing: If the median is closer to the smaller value/values mean will be greater than the median and median is closer to the bigger values median will be greater than

Statement 1:

Range is +ive
S= {0,5}--mean = median
S= {0,1,5}--median<mean
S= {0,3,5}--median>mean

So INSUFFICIENT

Statement 2:
Elements are not consecutive

S= {5,5}--mean = median
S= {1,3,6}--mean >median
S= {1,5,7}--median > mean

INSUFFICIENT

Combining also ..INSUFFICIENT

(E) is the answer

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