Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Set Q consists of n integers, of which the standard [#permalink]
10 Jul 2013, 22:01

2

This post received KUDOS

Expert's post

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

55% (02:34) correct
45% (01:02) wrong based on 107 sessions

Set Q consists of n integers, of which the standard deviation is D and the average (arithmetic mean) is M. If integer N is added to set Q, the standard deviation of the new set is less than D. Which of the following must be true?

I. N > M II. N < M III. N < D

A. I only B. II only C. III only D. II & III only E. None of the above

Re: Set Q consists of n integers, of which the standard [#permalink]
10 Jul 2013, 22:15

3

This post received KUDOS

Expert's post

bagdbmba wrote:

Set Q consists of n integers, of which the standard deviation is D and the average (arithmetic mean) is M. If integer N is added to set Q, the standard deviation of the new set is less than D. Which of the following must be true?

I. N > M II. N < M III. N < D

A. I only B. II only C. III only D. II & III only E. None of the above

Say Q={2, 3, 4} (consider a simple set). The standard deviation (D) will be very small (~1). The mean (M) is 3;

We want to add new element so that the standard deviation to decrease. Add the element which is equal to the mean. So, if N=3:

D will decrease --> condition satisfied. N=M --> discard I and II. N>D --> discard III.

Re: Set Q consists of n integers, of which the standard [#permalink]
10 Jul 2013, 22:51

Expert's post

Bunuel wrote:

bagdbmba wrote:

Set Q consists of n integers, of which the standard deviation is D and the average (arithmetic mean) is M. If integer N is added to set Q, the standard deviation of the new set is less than D. Which of the following must be true?

I. N > M II. N < M III. N < D

A. I only B. II only C. III only D. II & III only E. None of the above

Say Q={2, 3, 4} (consider a simple set). The standard deviation (D) will be very small (~1). The mean (M) is 3;

We want to add new element so that the standard deviation to decrease. Add the element which is equal to the mean. So, if N=3:

D will decrease --> condition satisfied. N=M --> discard I and II. N>D --> discard III.

Answer: E.

Hope it's clear.

Thanks Bunuel... Just couple of quick clarifications required:

1. For N>D--> S.D decreases but does that mean for N<D it won't be true always? Please clarify it.

2.What should be the approach for this type of problems? I mean is there any other way we can do it or the one you've shown is the most generic approach to solve...? _________________

Re: Set Q consists of n integers, of which the standard [#permalink]
10 Jul 2013, 23:03

Expert's post

bagdbmba wrote:

Bunuel wrote:

bagdbmba wrote:

Set Q consists of n integers, of which the standard deviation is D and the average (arithmetic mean) is M. If integer N is added to set Q, the standard deviation of the new set is less than D. Which of the following must be true?

I. N > M II. N < M III. N < D

A. I only B. II only C. III only D. II & III only E. None of the above

Say Q={2, 3, 4} (consider a simple set). The standard deviation (D) will be very small (~1). The mean (M) is 3;

We want to add new element so that the standard deviation to decrease. Add the element which is equal to the mean. So, if N=3:

D will decrease --> condition satisfied. N=M --> discard I and II. N>D --> discard III.

Answer: E.

Hope it's clear.

Thanks Bunuel... Just couple of quick clarifications required:

1. For N>D--> S.D decreases but does that mean for N<D it won't be true always? Please clarify it.

2.What should be the approach for this type of problems? I mean is there any other way we can do it or the one you've shown is the most generic approach to solve...?

1. The red part is wrong. If N=1000, the standard deviation will increase.

2. I think approach shown in my post is the easiest for this particular problem. _________________

Re: Set Q consists of n integers, of which the standard [#permalink]
10 Jul 2013, 23:26

Expert's post

Bunuel wrote:

bagdbmba wrote:

So why we're discarding the option III here?

The question is which of the options must be true?

Consider the example in my post. Does any of the options hold true for it?

Got it!

How I could know that which example set would be best to plug-in for soln? I mean is there any baseline to determine which set would be ideal to consider? _________________

Re: Set Q consists of n integers, of which the standard [#permalink]
21 Aug 2013, 13:23

This question is dealing with conceptual knowledge about standard deviation (SD): If SD is decreasing after adding a new number it means a number is added closer to the average arithmetic mean (AM) and that could be on the right side or left side on the number line of the AM, thus we can not say that this new number is less than or greater than M only we know that this number is closer to AM, further standard deviation is the measure of range +- density distribution of numbers around AM like most of the numbers are under umbrella of radius SD, it basically tells us that most of the numbers are around AM proximity in rage like 1.2 etc, so still we can not predict that new number is greater than SD or not, actually they are not comparable, and provided data is insufficient to calculate any number so 50 50 chances. Therefore answer should be E. _________________

Piyush K ----------------------- Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press--> Kudos My Articles: 1. WOULD: when to use?| 2. All GMATPrep RCs (New) Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

Re: Set Q consists of n integers, of which the standard [#permalink]
23 Aug 2013, 16:33

1

This post received KUDOS

bagdbmba wrote:

Bunuel wrote:

bagdbmba wrote:

So why we're discarding the option III here?

The question is which of the options must be true?

Consider the example in my post. Does any of the options hold true for it?

Got it!

How I could know that which example set would be best to plug-in for soln? I mean is there any baseline to determine which set would be ideal to consider?

Details:

Q= {2,3,4} Standard deviation : 1. mean = 3 2. difference: 1,0,-1 3. squaring: 1,0,1 4. mean again = (1+0+1)/3 = 2/3 5. root over (2/3) = standard deviation.

Now, Adding the man to the set Q . So {2,3,3,4} same way standard deviation: root over (1/2)

Certainly standard deviation decreases after adding mean 3.

The mean was M=3 and added number N=3 too and first standard deviation D= root over (2/3)

So N=M ( I and II both eliminated} we can see, N>D . So III eliminated. Nothing is must be true here...............

The example here {1,2,3} works well too, we can use it here conveniently.... start something like {1,2,3} or {2,3,4}...

Basics of this math is, add mean to a set and standard deviation will decrease certainly......... _________________

Asif vai.....

gmatclubot

Re: Set Q consists of n integers, of which the standard
[#permalink]
23 Aug 2013, 16:33

It’s been a long time, since I posted. A busy schedule at office and the GMAT preparation, fully tied up with all my free hours. Anyways, now I’m back...

Ah yes. Funemployment. The time between when you quit your job and when you start your MBA. The promised land that many MBA applicants seek. The break that every...

It is that time of year again – time for Clear Admit’s annual Best of Blogging voting. Dating way back to the 2004-2005 application season, the Best of Blogging...