Question

The prices of share of Company X and Company Y are given below. State, which company is more stable?

Company X	25	50	45	30	70	42	36	48	34	60
Company Y	10	70	50	20	95	55	42	60	48	80

Answer 1

Company X			Company Y
X	$\mathit{x}\mathbf{=}\mathit{X}\mathbf{-}\overline{\mathit{X}}$	x2	Y	$\mathit{y}\mathbf{=}\mathit{Y}\mathbf{-}\overline{\mathit{Y}}$	y2
25 50 45 30 70 42 36 48 34 60	−19 6 1 −14 26 −2 −8 4 −10 16	361 36 1 196 676 4 64 16 100 256	10 70 50 20 95 55 42 60 48 80	−43 17 −3 −33 42 2 −11 7 −5 27	1849 289 9 1089 1764 4 121 49 25 729
ΣX = 440		Σx2 = 1710	ΣY = 530		Σy2 = 5928

$$\begin{gathered} \overline{X}=\frac{\Sigma x^2}{N}=\frac{440}{10}=44 \\ {\sigma }_x=\sqrt{\frac{\Sigma x^2}{N}}=\sqrt{\frac{1710}{10}}=\sqrt{171}=13.08 \\ \mathrm{C}.\mathrm{V}.\mathrm{of}pricesofSharesof\mathrm{X}\mathrm{Co}.=\frac{{\sigma }_x}{\overline{X}}\times 100=\frac{13.08}{44}\times 100=29.72\% \end{gathered}$$


$$\begin{gathered} \overline{Y}=\frac{\Sigma Y}{N}=\frac{530}{10}=53 \\ {\sigma }_y=\sqrt{\frac{\Sigma y^2}{N}}=\sqrt{\frac{5928}{10}}=24.35 \\ \mathrm{C}.\mathrm{V}.ofpricesofShareofYco.=\frac{{\sigma }_y}{\overline{X}}\times 100=\frac{24.35}{53}\times 100=45.94\% \end{gathered}$$

As C.V of prices of shares of Co. X is less than that of the prices of shares of Co. Y therefore, price of share of Co. X is more stable.