Question

Set X consists of 100 numbers. The average (arithmetic mean) of set X is 10, and the standard deviation is 4.6. Which of the following two numbers, when added to set X, will decrease the set’s standard deviation by the greatest amount?
A. -100 and -100
B. -10 and -10
C. 0 and 0
D. 0 and 20
E. 10 and 10

Answer 1

Answer:

E. 10 and 10

Step-by-step explanation:

Standard Deviation is the square root of sum of square of the distance of observation from the mean.

$Standard deviation(\sigma) = \sqrt{\frac{1}{n}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}} }$

where, $\bar{x}$ is mean of the distribution.

Here, since standard deviation is the ratio of the distance from the mean and sample size. So for decreasing the standard deviation we should keep numerator constant and increasing the denominator.

This can be only possible in option (E).

Hence, only Option (E) is correct.