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What is median - average?

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by LulaBrazilia » Mon Mar 10, 2014 5:37 pm
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
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by Patrick_GMATFix » Mon Mar 10, 2014 5:47 pm
A string of numbers at constant intervals (such as consecutive multiples of 5) is called an arithmetic sequence. One property of such a sequence is that its average equals its median. So the difference between median and average is 0.

The answer is B. I go through the question in detail in the full solution below (taken from the GMATFix App).

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by PythaGURUS » Mon Mar 10, 2014 8:13 pm
LulaBrazilia 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
Hi LulaBrazilia,

This questions tests the concept of Arithmetic Progressions.

An Arithmetic Progression or an AP is a sequence where the difference between any two consecutive terms is same. For ex: 2,4,6,8,10.. is an AP because every next term is obtained by adding a common difference of 2 to the previous term.

First 10 multiples of 5 also make an AP.

Now you might want to remember this as a general rule on GMAT:

For an AP, the Mean(Avg.) is the same as Median(Middle Term) irrespective of the common difference or the total terms in the sequence.

Mean=Median for an Arithmetic Progression.

Hence their difference should be zero.
Correct option should be (B)

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by [email protected] » Tue Mar 11, 2014 12:30 am
Hi LulaBrazilia,

Sometimes the easiest way to answer a Quant question is to "brute force" it - just do the work on the pad and get the answer as quickly as possible.

Here, we're asked to compare the AVERAGE of the first 10 positive multiples of 5 to the MEDIAN of the first 10 positive multiples of 5.

The numbers: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

To get the average, rather than add these numbers in order, we can "bunch" them.
5+50 = 55
10+45 = 55
etc.
So we have 5 sets of 55 = 275

Average = 275/10 = 27.5

The median in a set of 10 terms is the average of the 5th and 6th values. The average of 25 and 30 is...

55/2 = 27.5

So, the average - the median = 27.5 - 27.5 = 0

Final Answer: B

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by Jeff@TargetTestPrep » Mon Dec 11, 2017 6:55 am
LulaBrazilia 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
To answer this question we can use the following rule:

When we have an evenly spaced set of numbers, the mean and the median are equal. Recall that in an evenly spaced set of numbers there is a common difference between consecutive terms in the set. For example, consecutive integers, consecutive odd integers, consecutive even integers, and consecutive multiples of any given number are all examples of evenly spaced sets.

Thus the answer is 0.

Answer: B

Jeffrey Miller
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