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If m is the average (arithmetic mean) of the first 10 [#permalink]

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27 Feb 2012, 14:40

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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 ?

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

10 sec approach:

The first 10 positive multiples of 5 is an evenly spaced set. 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.

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]

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20 Jun 2013, 23:00

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As it is a Evenly spaced set, the MEAN and MEDIAN will be same for the set.

So, the MEAN or MEDIAN for such sets will be -> Avg. of First term and last term. i.e, (5+50)/2 in this case. Blindly we can say answer is zero, because the Q asks the difference between MEAN and MEDIAN for Evenly spaced set(Basic Thumb rule)...

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:

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]

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11 Sep 2014, 01:45

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 ?

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]

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24 Sep 2015, 20:58

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Re: If m is the average (arithmetic mean) of the first 10 [#permalink]

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06 Aug 2016, 04:01

Using the rule => For any AP series the mean = median So the difference = 0 Additionally Mean = Median = A(V) = First term+last term /2 = 55/2 = 27.5 Hence=> Mean = median = 27.5

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Re: If m is the average (arithmetic mean) of the first 10
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06 Aug 2016, 04:01

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