Question

Calculate the Standard deviation from the following values:8 , 9, 15, 23, 5, 11, 19, 8, 10, 12.

Answer 1

Values (X)	$\mathit{x}\mathbf{=}\left|\mathit{X}\mathbf{-}\overline{\mathit{X}}\right|$	x2
8	−4	16
9	−3	9
15	3	9
23	11	121
5	−7	49
11	−1	1
19	7	49
8	−4	16
10	−2	4
12	0	0
ΣX=120		Σx2=274

$$\begin{gathered} Mean,\overline{\mathrm{X}}=\frac{\Sigma X}{N}=\frac{120}{10}=12 \\ \mathrm{Standard}\mathrm{deviation}\left(\sigma \right)=\sqrt{\frac{\Sigma x^2}{N}} \\ or,\left(\sigma \right)=\sqrt{\frac{274}{10}} \\ or,\left(\sigma \right)=\sqrt{27.4} \\ \Rightarrow \left(\sigma \right)=5.23 \end{gathered}$$

Hence, the standard deviation of the above series is 5.23