Question

Let n ³ 3 .A list of numbersx_1, x₂,.........x_n has mean m and standard deviation s . A new list of numbers y₁, y₂,..........y_n is made as follows : and y_j = x for j = 3,4,.......n . The mean and the standard deviation of the list are. Then which of the following is necessarily true?

• A. $\mu =\hat{\mu }$ and $\sigma \le \hat{\sigma }$
• B. $\mu =\hat{\mu }$ and $\sigma \ge \hat{\sigma }$
• C. $\sigma =\hat{\sigma }$
• D. $\mu \ne \hat{\mu }$

Answer 1

The correct option is B

$\mu =\hat{\mu }$ and $\sigma \ge \hat{\sigma }$