Question

The standard deviation of $10$ observations $111,211,311,...,1011$ is

• A. $250$
• B. $100\sqrt{3}$
• C. $300$
• D. $50\sqrt{33}$

Answer 1

The correct option is D $50\sqrt{33}$

Let $x_i=1,2,3,...,10$
Then, given observations can be written as $y_i=100x_i+11$
Standard deviation can be calculated as $\sigma \left(y_i\right)=100\sigma \left(x_i\right)$
$\sigma \left(x_i\right)=\sqrt{\frac{10\times 11\times 21}{10\times 6}-{\left(\frac{10\times 11}{2\times 10}\right)}^2}$
$=\frac{\sqrt{33}}{2}$
$\Rightarrow \sigma \left(y_i\right)=50\sqrt{33}$