Question

The following table gives marks obtained by 7 students of a class. Find out standard deviation of the marks.
40, 42, 38, 44, 46, 48, 50

Answer 1

S. No.	Marks (X)	Deviation $$\begin{gathered} \left(\mathit{x}\mathbf{=}\mathit{X}\mathbf{-}\overline{\mathbf{X}}\right) \\ \overline{\mathbf{X}}\mathbf{=}\mathbf{44} \end{gathered}$$	Square of the deviation ${\mathit{x}}^{\mathbf{2}}\mathbf{=}{\left(\mathit{X}\mathbf{-}\overline{\mathbf{X}}\right)}^{\mathbf{2}}$
1 2 3 4 5 6 7	40 42 38 44 46 48 50	−4 −2 −6 0 2 4 6	16 4 36 0 4 16 36
N = 7	ΣX = 308		Σx2 = 112

$$\begin{gathered} \mathrm{Mean}\left(\overline{\mathrm{X}}\right)=\frac{\mathit{\Sigma }\mathit{X}}{\mathit{N}}=\frac{308}{7}=44 \\ \mathrm{Standard}\mathrm{deviation}(\mathrm{\sigma })=\sqrt{\frac{x^2}{N}}=\sqrt{\frac{112}{7}}=\sqrt{16}=4 \end{gathered}$$
Hence, standard deviation of the marks is 4.