Set \(X\) consists of \(100\) numbers. The average (arithmetic mean) of set \(X\) is \(10,\) and the standard deviation

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: E

Source: Magoosh