Question

Calculate Mean and Standard Deviation of income of 8 employees of a firm:

Income (₹):

100

120

140

120

180

140

120

150

Answer 1

S. No. (X)	Deviation $$\begin{gathered} x=X\mathit{-}\overline{X} \\ \overline{X}=133.75 \end{gathered}$$	x2
100 120 140 120 180 140 120 150	−33.75 −13.75 6.25 −13.75 46.25 6.25 −13.75 16.25	1139.06 189.06 39.06 189.06 2139.06 39.06 189.06 264.06
ΣX= 1070		Σx2 = 4187.48

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }X}{N}=\frac{1070}{8}=133.75 \\ SD=\sqrt{\frac{\mathrm{\Sigma }{x}^2}{N}}=\sqrt{\frac{4187.48}{8}}=\sqrt{523.43}=22.87 \end{gathered}$$
Thus, mean standard deviation is 22.87.