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A certain list of 100 data has an average (arithmetic mean) of 6 and a standard deviation of d, where d is positive.

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by BTGmoderatorDC » Thu Feb 13, 2020 5:18 pm
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


OA E

Source: Manhattan Prep
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Re: A certain list of 100 data has an average (arithmetic mean) of 6 and a standard deviation of d, where d is positive.

by Jay@ManhattanReview » Thu Feb 13, 2020 9:11 pm
BTGmoderatorDC wrote: ↑
Thu Feb 13, 2020 5:18 pm
 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

OA E

Source: Manhattan Prep
In a simpler term, Standard Deviation (SD) of a dataset is a measure of deviations of a data set w.r.t. their average (arithmetic mean).

Though the computation of SD is beyond the scope of the GMAT, its analysis and interpretation are.

So, we are given that there are 100 terms that have their average = 6 and SD = d.

Note that closer the value of a data to the average, lesser is its deviation w.r.t. that of terms that are relatively far from the mean. So, the ideal value of the two terms would be = average (mean) = 6 (given). Since with the values of 6, the terms will not be any deviation w.r.t. mean; their individual deviations would be 0, thereby the SD of 102 terms would be less than that of the SD of 100 terms.

Option E answers this.

The correct answer: E

Hope this helps!

-Jay
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