Question

$\{9,12,15,18,21\}$
Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?
I. $14,16$
II. $9,21$
III. $15,100$

• A. II only
• B. III only
• C. I and II
• D. II and III
• E. I, II, and III

Answer 1

Answer: (D)

II and III

Fortunately, you do not need to perform any calculations to answer this question.The mean of the set is $15$. Take a look at each Roman Numeral:

I. The numbers $14$ and $16$ are both very close to the mean $\left(15\right)$. Additionally, they are closer to the mean than four of the numbers in the set, and will reduce the spread around the mean.This pair of numbers will reduce the standard deviation of the set.

II. The numbers $9$ and $21$ are relatively far away from the mean $\left(15\right)$. Adding them to the list will increase the spread of the set and increase the standard deviation.

III. While adding the number $15$ to the set would actually decrease the standard deviation (because it is the same as the mean of the set), the number $100$ is so far away from the mean that it will greatly increase the standard deviation of the set. This pair of numbers will increase the standard deviation.