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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

A certain list has an average of 6 and a standard deviation [#permalink]

Show Tags

18 Jul 2010, 12:33

9

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

69% (01:42) correct
31% (01:08) wrong based on 321 sessions

HideShow timer Statistics

A certain list has an average of 6 and a standard deviation of d (d is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than d?

A certain list has an average of 6 and a standard deviation of d (d is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than d?

a. (-6;0) b. (0;0) c. (0;6) d. (0;12) e. (6;6)

OA Later

"Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values."

So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.

According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.

Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.

Thank you Bunuel, I just add 1 following remark. E is only correct if we take into account that d is positive. In case of d=0, the SD remains the same.
_________________

A certain list of 100 data has an average of 6 and standard deviation of d where d is positive. Which of the following pairs of data, when added to the list must result in a list of 102 data with the standard deviation less than d? (A) 0 and 6 (B) 0 and 12 (C) 0 and 0 (D) -6 and 0 (E) 6 and 6

A certain list of 100 data has an average of 6 and standard deviation of d where d is positive. Which of the following pairs of data, when added to the list must result in a list of 102 data with the standard deviation less than d? (A) 0 and 6 (B) 0 and 12 (C) 0 and 0 (D) -6 and 0 (E) 6 and 6

Option E offers two numbers equal to the mean while other options (including C) offer number(s) different from the mean. Adding two numbers which are closest to the mean (option E in our case ) will shrink the set most, thus decreasing SD by the greatest amount.

Re: A certain list has an average of 6 and a standard deviation [#permalink]

Show Tags

11 Jul 2012, 09:49

+1 E

This is a conceptual question. If you add more data to the average, more data will be closer to the average. Hence, the standard deviation is lower.
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

Tricky question! Is there an alternative solution?

This is a conceptual question. There is no so-called process that you can follow. You need to understand how SD is related to the average and the number of terms (through the SD formula). Once you do, you solve it by just looking at the options. Check out the links given above.
_________________

Re: A certain list has an average of 6 and a standard deviation [#permalink]

Show Tags

24 Dec 2014, 12:10

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: A certain list has an average of 6 and a standard deviation [#permalink]

Show Tags

17 May 2015, 16:51

Could someone explain what the question means by "must result in a list of 102 data" - that threw me off and I ended up completely ignoring that piece of information and was still able to get the question right but found it to be confusing.

Could someone explain what the question means by "must result in a list of 102 data" - that threw me off and I ended up completely ignoring that piece of information and was still able to get the question right but found it to be confusing.

It just means that with the addition of the two numbers, there will be 102 numbers in the list. So originally the list had 100 data points. In fact, the same question given here clarifies this: a-certain-list-has-an-average-of-6-and-a-standard-deviation-97473.html#p769038 Since the question is conceptual, it doesn't matter much what the exact number of numbers are. It is just given to clarify that only 2 numbers were added and all others were retained.
_________________

Re: A certain list has an average of 6 and a standard deviation [#permalink]

Show Tags

19 Jun 2016, 02:01

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...