Bunuel wrote:

Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?

A. {2, 10}

B. {10, 18}

C. {7, 13}

D. {9, 11}

E. {16, 16}

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:This is a very tricky problem. Starting list has mean = 10 and standard deviation of 1.5.

(A) {2, 10} — these two don’t have a mean of 10, so adding them will change the mean; further, one number is “far away”, which will wildly decrease the mean, increasing the deviations from the mean of almost every number on the list, and therefore increasing the standard deviation. WRONG

B. {10, 18} — these two don’t have a mean of 10, so adding them will change the mean; further, one number is “far away”, which will wildly increase the mean, increasing the deviations from the mean of almost every number on the list, and therefore increasing the standard deviation. BTW, (A) & (B) are essentially the same change — add the mean and add one number eight units from the mean. WRONG

C. {7, 13} — centered on 10, so this will not change the mean. Both of these are a distance of 3 units from the mean, and this is larger than the standard deviation, so it increases the size of the typical deviation from the mean. WRONG

D. {9, 11} — centered on 10, so this will not change the mean. Both of these are a distance of 1 units from the mean, and this is less than the standard deviation, so it decreases the size of the typical deviation from the mean. RIGHT

E. {16, 16} — these are two values far away from everything else, so this will wildly increase the standard deviation. WRONG

Answer = D.

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