BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

PS--SD again

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 179
Joined: Tue Jan 08, 2008 7:23 pm
Thanked: 11 times
GMAT Score:590
by nitya34 » Tue Jul 21, 2009 6:12 am
Set X consists of 100 numbers. The average (arithmetic mean) of set X is 10, and the standard deviation is 4.6. Which of the following two numbers, when added to set X, will decrease the set’s standard deviation by the greatest amount?

-100 and -100;
-10 and -10;
0 and 0;
0 and 20;
10 and 10


OA-[spoiler]E.....>10 and 10[/spoiler]

source:www.magoosh.com

try the DS section of magoosh
Many of the great achievements of the world were accomplished by tired and discouraged men who kept on working.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 345
Joined: Wed Mar 18, 2009 6:53 pm
Location: Sao Paulo-Brazil
Thanked: 12 times
GMAT Score:660

by shibal » Tue Jul 21, 2009 6:15 am
10 and 10 or -10 and -10?

IMO 10and10
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 85
Joined: Tue Sep 02, 2008 12:13 am
Thanked: 1 times
GMAT Score:650

by vzzai » Fri Jun 03, 2011 9:16 pm
Could someone please provide detailed explanation?

I was under the opinion that if the mean is reduced by maximum then the SD will reduce by maximum. So, I was thinking that "-100 and -100" reduce the mean by greatest value. I'm wrong. Please explain.
Thank you,
Vj
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1448
Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members
Location: India
Thanked: 375 times

by Frankenstein » Fri Jun 03, 2011 9:59 pm
Hi,
Let the elements be x1,x2,...x100, mean be 'm' and standard deviation be 'd'.
d^2=[(x1-m)^2+(x2-m)^2+...(x100-m)^2]/n = [(x1^2+x2^2+...x100^2)-nm^2]/n.
Lets denote (x1^2+x2^2+...x100^2) by p.
So, nd^2 = p-nm^2 => d^2=(p/n)-m^2 => (4.6)^2 = p/100 - 10^2 => p=12116
Options D and E will not change the mean but D adds 20^2 to p where as E adds (10^2)+(10^2) to p. So, 'd' will less in E compared to D.
For Op E, d^2= (p+200)/102 - 10^2 =~ (p/102 - 98)
For Op A, d^2= (p+2.10^4)/102 - (800/102)^2
For op B, d^2= (p+200)/102 - (980/102)^2
For op C, d^2= (p/102) - (1000/102)^2 =~ (p/102 - 96)

Clearly d^2 is smallest in op E.
Hence, E

There is theoretical approach to solve this. S.D is nothing but the variation from the mean. The lower the SD the closer are the points to the mean. Adding numbers far from the mean increases SD. As we come closer to the mean, the distribution curve shrinks making SD smaller as we move close to the mean. So, adding mean values to the set actually decreases SD to the maximum extent.
Cheers!

Things are not what they appear to be... nor are they otherwise
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1309
Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members
Location: India
Thanked: 310 times
GMAT Score:750

by cans » Sat Jun 04, 2011 8:56 am
Set X consists of 100 numbers. The average (arithmetic mean) of set X is 10, and the standard deviation is 4.6. Which of the following two numbers, when added to set X, will decrease the set's standard deviation by the greatest amount?

-100 and -100;
-10 and -10;
0 and 0;
0 and 20;
10 and 10
avg of 100=10. Thus sum is 1000. sum of 102 numbers = (1000+a+b)/102
a)-100 and -100, mean is nearly equal to 8. But as two numbers -100,-100 are too far away from the mean, it will increase the s.d.
b)-10,-10 will effect mean a little, but because numbers are far from mean, thus s.d. will increase
similar for c) and d)
for e)10,10. Mean remains same and thus maximum decrease in s.d.
IMO E
If my post helped you- let me know by pushing the thanks button ;)

Contact me about long distance tutoring!
[email protected]

Cans!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1