Question

Find the standard deviation for the following data: 3, 5, 6, 7, 10, 12, 15, 18.

Answer 1

Values (X)	$\mathit{x}\mathbf{=}\mathit{X}\mathbf{-}\overline{\mathbf{X}}$	x2
3	−6.5	42.25
5	−4.5	20.25
6	−3.5	12.25
7	−2.5	6.25
10	.5	.25
12	2.5	6.25
15	5.5	30.25
18	8.5	72.25
ΣX=76		Σx2=190

$$\begin{gathered} Mean,\overline{X}=\frac{\Sigma X}{N}=\frac{76}{8}=9.5 \\ \mathrm{Standard}\mathrm{deviation}\left(\sigma \right)=\sqrt{\frac{\Sigma x^2}{N}} \\ or,\left(\sigma \right)=\sqrt{\frac{190}{8}} \\ or,\left(\sigma \right)=\sqrt{23.75} \\ \Rightarrow \left(\sigma \right)=4.87 \end{gathered}$$

Hence, standard deviation of the above series is 4.87