BANON wrote:

If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M – m ?

(A) –5

(B) 0

(C) 5

(D) 25

(E) 27.5

Responding to a pm:

m = mean = (5 + 10 + 15 + ....+ 50)/10 = 27.5

M = median

Median of 10 numbers will be the average of the middle two numbers i.e. 5th and the 6th numbers. 5th number = 25, 6th number = 30. Median = (25+30)/2 = 27.5

m - M = 0

This solution is the simplest I could think of which uses nothing but the definition of mean and median.

Notice that actually, you will do far less to arrive at the answer.

Mean of an arithmetic progression is the middle value in case there are odd number of terms and average of middle 2 values if there are even number of terms.

Median of an arithmetic progression is the middle term in case there are odd number of terms and average of middle 2 values if there are even number of terms.

So basically, they are both same in case of an arithmetic progression.

I would suggest you to check out the following posts. They discuss these concepts in detail:

http://www.veritasprep.com/blog/2012/04 ... etic-mean/http://www.veritasprep.com/blog/2012/05 ... eviations/http://www.veritasprep.com/blog/2012/05 ... on-median/
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Karishma

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