Question

Let $x_1,x_2,\dots \dots \dots x_n$ be 𝑛 observation and $\overline{x}$ be their arithmetic mean. The formula for the standard deviation is given by

• A. $\sum (x_i-\overline{x}{)}^2$
• B. $\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{n}}$
• C. $\sqrt{\frac{\sum x_i^2}{n}+\overline{x^2}}$
• D. $\frac{\sum (x_i-\overline{x}{)}^2}{n}$

Answer 1

The correct option is B $\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{n}}$

The formula for standard deviation is Hence,

$\sigma =\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{n}}$

Option (𝐶) is correct.