sanju09 wrote:A certain list of 100 data has an average 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 0f 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
[spoiler]Source:
www.avenuesabroad.org or gmatprep[/spoiler]
SD describes how much the data deviates from the mean. A high SD means that the data is spread far from the mean; in other words, it deviates
more from the mean. A low SD means that the data is positioned close to the mean; in other words, it deviates
less from the mean. A SD of 0 means that each piece of data is equal to the mean; in other words, the data doesn't deviate at all from the mean.
Since d>0, we know that the data is deviating from the mean. To guarantee a smaller SD, we need an answer choice that will introduce data closer to the mean. Answer choice E leaves the mean unchanged (the new average would be (600+6+6)/102 = 612/102 = 6) but adds two pieces of data equal to the mean; the result is that more of the data will be deviating
less from the mean, so the SD will have to decrease.
The correct answer is
E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
