Bunuel wrote:
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
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION:As discussed
HERE, the standard deviation of a set measures the deviation from the mean. A low standard deviation indicates that the data points are very close to the mean whereas a high standard deviation indicates that the data points are spread far apart from the mean.
When we add numbers that are far from the mean, we are stretching the set and hence, increasing the SD. When we add numbers which are close to the mean, we are shrinking the set and hence, decreasing the SD.
Therefore, adding two numbers which are closest to the mean will shrink the set the most, thus decreasing SD by the greatest amount.
Numbers closest to the mean are 75 and 75 (they are equal to the mean) and thus adding them will decrease SD the most.
Answer: D. _________________