Home » » Find the standard deviation of 2, 3, 5 and 6

Find the standard deviation of 2, 3, 5 and 6

Question

Find the standard deviation of 2, 3, 5 and 6

Options

A) √6

B) √10

C) √$$\frac{2}{5}$$

D) √$$\frac{5}{2}$$

The correct answer is D.

Explanation:

$$\begin{array}& x & x - \bar{x} & (x - \bar{x})^2 \\2 & -2 & 4 \\ 3 & -1 & 1 \\ 5 & 1 & 1 \\ 6 & 2 & 4\\ \hline \sum x = 16 & & \sum (x - \bar{x}^2) = 0 \end{array}$$
___________________________________
$$\bar{x}$$ = $$\frac{\sum x }{N}$$
= $$\frac{16}{4}$$
= 4
S = $$\sqrt{\frac {(x - \bar{x})^2}{N}}$$
= $$\sqrt{\frac {(10)}{4}}$$
= $$\sqrt{\frac {(5)}{2}}$$

Dicussion (1)

• $$\begin{array}& x & x - \bar{x} & (x - \bar{x})^2 \\2 & -2 & 4 \\ 3 & -1 & 1 \\ 5 & 1 & 1 \\ 6 & 2 & 4\\ \hline \sum x = 16 & & \sum (x - \bar{x}^2) = 0 \end{array}$$
___________________________________
$$\bar{x}$$ = $$\frac{\sum x }{N}$$
= $$\frac{16}{4}$$
= 4
S = $$\sqrt{\frac {(x - \bar{x})^2}{N}}$$
= $$\sqrt{\frac {(10)}{4}}$$
= $$\sqrt{\frac {(5)}{2}}$$