Set S has a mean of 10 and a standard deviation of 1.5. We are going

Question

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 .

Bunuel · Accepted Answer

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.

hoangyen · Answer

D

Since 9 and 11 added to set S will not change the mean, and the distance from the mean to them is less than the standard deviation, the S.D will decrease.

AverageGuy123 · Answer

The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 10,the values (9,11) are closer than others.
Hence Answer should be D

sytabish · Answer

Hi,

To decrease the standard deviation, we should add values that are closer to the mean. The best bet would be two 10s. However, we don't have two 10s in the options. The next best values are 9, 11 , both within 1 point of the mean. Rest all far away and will increase the SD rather than decreasing it.

Thanks!

Temurkhon · Answer

Numbers closer to Mean, i.e 10 will decrease SD most

D

naveeng15 · Answer

Only set which doesn't affect the mean is (9,11) 
Standard deviation = how dispersed the set is this the decrease in standard deviation means the new numbers should be near the mean hence the two numbers are (9,11)

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Set S has a mean of 10 and a standard deviation of 1.5. We are going

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