Events & Promotions
|
|
GMAT Club Daily Prep
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2212:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
Updated on: 10 Oct 2019, 04:45
Originally posted by Gmatter111 on 08 Dec 2009, 03:54.
Last edited by Bunuel on 10 Oct 2019, 04:45, edited 4 times in total.
Last edited by Bunuel on 10 Oct 2019, 04:45, edited 4 times in total.
Renamed the topic and edited the question.
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
78% (00:57) correct
22%
(01:26)
wrong
based on 1493
sessions
History
Date
Time
Result
Not Attempted Yet
A certain list of 100 data has an average (arithmetic mean) of 6 and a 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 standard deviation less than d ?
A. -6 and 0
B. 0 and 0
C. 0 and 6
D. 0 and 12
E. 6 and 6
A. -6 and 0
B. 0 and 0
C. 0 and 6
D. 0 and 12
E. 6 and 6
Every tricky question should trigger a follow up quiz.
Build that habit with
GMAT Club Forum Quiz →.
18 Nov 2010, 01:14
Kudos
Bookmarks
itsreallytime
Yes, mean won't be the same for A, B, and C but as it will differ from 6 very little then the calculations above will still hold true, so it doesn't really matter.
As for the question, GMAT SD questions are fairly straightforward and don't require actual calculation of SD, they are about the general understanding of the concept.
So we have:
A certain list of 100 data has an average (arithmetic mean) of 6 and a 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 standard deviation less than d?
A. -6 and 0
B. 0 and 0
C. 0 and 6
C. 0 and 12
D. 6 and 6
"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.
Answer: E.
For more on this issue please check Standard Deviation chapter of Math Book (link in my signature) and the following two topics for practice:
https://gmatclub.com/forum/ps-questions- ... 85897.html
https://gmatclub.com/forum/ds-questions- ... 85896.html
Hope it helps.
08 Dec 2009, 05:33
Kudos
Bookmarks
Gmatter111
Logically, SD of a set will decrease if you add numbers which are equal to its mean. Thus the answer should be E.
I will however provide you with mathematical reasoning to justify the above statement.
S.D. for hundred numbers = d = \(\sqrt{\frac{S}{100}}\) where 'S' is sum of the squares of the difference between each number and the mean.
Now let the two numbers added be 'x' and 'y'.
S.D after adding the two numbers will be = \(\sqrt{\frac{S}{102}+\frac{(x-6)^2 + (y-6)^2}{102}}\)
Now it is obvious that \(\frac{S}{102}\) will be less than \(\frac{S}{100}\). Also, the minimum value of \(\frac{(x-6)^2 + (y-6)^2}{102}\) will be 0 when both 'x' and 'y' are equal to 6.
Thus if the two numbers added are equal to the mean, the SD of the set must decrease. (Unless of course SD of the set was 0 to start with (not in our case) and then in that case SD will remain constant).
Answer : E
