Question

Find out standard deviation of the savings of the following 10 persons:

Persons	1	2	3	4	5	6	7	8	9	10
Savings (₹)	114	108	100	98	101	109	117	119	121	126

Answer 1

Persons	Savings (X)	Deviation $\left(\mathit{x}\mathbf{=}\mathbf{X}\mathbf{-}\overline{\mathbf{X}}\right)$ $\overline{\mathbf{X}}$=111.3	Square of the deviation x2
1 2 3 4 5 6 7 8 9 10	114 108 100 98 101 109 117 119 121 126	2.7 −3.3 −11.3 −13.3 −10.3 −2.3 5.7 7.7 9.7 14.7	7.29 10.89 127.69 176.89 106.09 5.29 32.49 59.29 94.09 216.09
N = 10	ΣX = 1113		Σx2 = 836.1

$$\begin{gathered} \mathrm{Mean}\left(\overline{X}\right)=\frac{\mathrm{\Sigma }X}{N}=\frac{1113}{10}=111.3 \\ \mathrm{Standard}\mathrm{deviation}(\sigma )=\sqrt{\frac{\mathrm{\Sigma }{x}^2}{N}}=\sqrt{\frac{836.1}{10}}=\sqrt{83.61}=9.14 \end{gathered}$$

Hence, standard deviation of the savings is 9.14