A certain list of 200 test scores has an average (arithmetic mean) of 90 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 202 test scores with a standard deviation less than d ?
Choices:
A) 80 and 80
B) 80 and 85
C) 90 and 90
D) 85 and 85
E) 85 and 90
The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.   So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.   According to the aboveadding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.   Closest to the mean are 90 and 90 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD most.   Answer: 90 and 90.
<result>C</result>
A certain list of 200 test scores has an average (arithmetic mean) of 90 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 202 test scores with a standard deviation less than d ?