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a list 0f 102 data

by sanju09 » Fri Sep 17, 2010 3:01 am
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



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by GMATGuruNY » Fri Sep 17, 2010 3:28 am
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



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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.
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