AAPL wrote:Veritas Prep

A certain list of 300 test scores has an arithmetic mean of 75 and a standard deviation of \(d\), where \(d\) is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than \(d\)?

A. 75 and 80
B. 80 and 85
C. 70 and 75
D. 75 and 75
E. 70 and 80

OA D

Nice question:

Standard deviation (SD) is a number used to tell how measurements for a group are spread out from the average (mean), or expected value. A low standard deviation means that most of the numbers are close to the average. A high standard deviation means that the numbers are more spread out.

Ref. to the phrase, "A low standard deviation means that most of the numbers are close to the average," Since with the inclusion of two additional scores, we want less than d SD, the additional scores must be close to the average (75). The best is equal to the average.

The best option is Option D: both the scores are equal to average. The SD of the 302 scores would be less than d.

The correct answer: D

Hope this helps!

-Jay
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Jay@ManhattanReview wrote: Nice question:

It's a near-verbatim copy of this GMATPrep question, they just changed a couple of numbers:

https://www.beatthegmat.com/standard-de ... 45521.html

AAPL wrote:Veritas Prep

A certain list of 300 test scores has an arithmetic mean of 75 and a standard deviation of \(d\), where \(d\) is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than \(d\)?

A. 75 and 80
B. 80 and 85
C. 70 and 75
D. 75 and 75
E. 70 and 80

OA D

The standard deviation is a measure of spread of the data about the mean. Adding data values that are far from the mean make the standard deviation larger. Adding data values equal to the mean makes the spread of the data (i.e., the standard deviation) smaller.

Since the mean is 75, we see that when we add 75 and 75 to the list, the standard deviation must decrease. Note: Depending on the value of d, the other choices might or might not decrease the standard deviation.

Answer: D