Question

The standard deviation of a variable $x$ is $10$. Then, the standard deviation of $5x+50$ is

• A. $50$
• B. $550$
• C. $500$
• D. $10$

Answer 1

The correct option is A

$50$

Explanation for correct option:

Find the standard deviation,

standard derivation of $x=10$

standard deviation of $x$$=\sqrt{\left(\mathrm{variance}\right)\left(\mathrm{x}\right)}$

$$\begin{gathered} 10=\sqrt{\mathrm{variance}\left(\mathrm{x}\right)} \\ {\left(10\right)}^2=\mathrm{variance}\left(\mathrm{x}\right) \\ \Rightarrow \mathrm{variance}\left(\mathrm{x}\right)=100 \end{gathered}$$

standard derivation of $5x+50$$=\sqrt{\mathrm{variance}(50+5\mathrm{x})}$

standard derivation of $5x+50$$=\sqrt{\mathrm{variance}\left(5\mathrm{x}\right)}$ [variance of constant$=0$]

standard derivation of $5x+50$$=\sqrt{5^2\times \mathrm{variance}\left(\mathrm{x}\right)}$

$$\begin{gathered} =5\sqrt{100} \\ =5\times 10 \\ =50 \end{gathered}$$

Hence, option (A), $50$ is correct answer.