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how do we know all the elements in S are positive? what if we have -3, -6, -9, 0, 3, etc?

REVISED VERSION OF THIS QUESTION IS BELOW:

Is the mean of set S greater than its median?

(1) Set S consist of consecutive multiples of 3 --> set S is evenly spaced. One of the most important properties of evenly spaced set (aka arithmetic progression) is: in any evenly spaced set the arithmetic mean (average) is equal to the median. So, the mean of S = the median of S. Sufficient.

(2) The sum of all terms of set S is 75 --> if S={75} then mean=median but if S={0, 0, 75} then (mean=25)>(0=median). Not sufficient.

If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values

mundasingh123 wrote:

what if there is an even number of elements in the Set S,For example 27,30,33,36 Mean=31.5 Median=30 or 33 then?

1. Let set is two number (3,6) mean=4.5, median=4.5 now let take 3 nos. (15, 18, 21) mean=18, Median=18 now lets take a bigger set (-12, -9,-6,-3,0,3,6,9) Median = -1.5, Mean = -12/8= -3/2 = -1.5

A is answer Golden rule for Consecutive integers is already explained just a addition

True, as Bunuel said, Mean=Median or evenly spaced sets, so (i) sufficient in (ii) the sets have a sum of 75 ; we can have many combinations to do so (0,0,75),(25,25,25), etc..-insufficient (A)wins
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