Question

Let $x_1,x_2,x_3,.....x_n$ be n observations with mean is $\overline{x}$ and variance is ${\sigma }^2$
Statement 1 : The variance of $5x_1,5x_2,5x_3,....,5x_{n}is25{\sigma }^2$
Statement 2 : The mean of $5x_1,5x_2,.....5x_{n}is10\overline{x}$
Then which of the following is correct

• A. Statement – 1 is true, and Statement – 2 is false
• B. Statement – 1 is false, and Statement – 2 is true
• C. Statement – 1, Statement – 2 are true and Statement – 2 is correct explanation of Statement – 1
• D. Statement – 1, Statement – 2 are true and Statement – 2 is not correct explanation of Statement – 1

Answer 1

The correct option is A Statement – 1 is true, and Statement – 2 is false

Mean of $(5x_1,5x_2,....5x_n)=\frac{5x_1+5x_2+....+5x_n}{n}=5\overline{x}$
Variance $(5x_1,5x_2,......5x_n)=25{\sigma }^2$
$\therefore$ Statement – 1 is true and Statement – 2 is false.