Question

The standard deviation of $n$ observations $x_1, x_2, \ldots, x_n$ is given by

• A. $\sigma=\sqrt{\displaystyle\sum_{i=1}^n\left(x_i-\bar{x}\right)^2}$
• B. $\sigma=\sqrt{\displaystyle\sum_{i=1}^n\left(x_i+\bar{x}\right)^2}$
• C. $\sigma=\sqrt{\frac{1}{n} \displaystyle\sum_{i=1}^n\left(x_i-\bar{x}\right)^2}$
• D. $\sigma=\sqrt{\frac{1}{n} \displaystyle\sum_{i=1}^n\left(x_i+\bar{x}\right)^2}$

Answer 1

Answer: (C)

The standard deviation, usually denoted by $\sigma$, is given by
$\sigma=\sqrt{\frac{1}{n} \displaystyle\sum_{i=1}^n\left(x_i-\bar{x}\right)^2}$