What is median - average?

Question

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

Patrick_GMATFix · Answer

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).

-Patrick

PythaGURUS · Answer

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)

Academics Team,
PythaGURUS education

Regards,

PythaGURUS Education

MBA Admissions Consulting

www.pythagurus.com

Rich.C@EMPOWERgmat.com · Answer

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

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Jeff@TargetTestPrep · Answer

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)

Academics Team,
PythaGURUS education

Regards,

PythaGURUS Education

MBA Admissions Consulting

www.pythagurus.com

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