Question

From the prices of shares X and Y below, find out which is more stable in value :

$\begin{array}{ccccccccccc}X& 35& 54& 52& 53& 56& 58& 52& 50& 51& 49\\ Y& 108& 107& 105& 105& 106& 107& 104& 103& 104& 101\end{array}$

Answer 1

$\begin{array}{cccccc}& & & & & \\ X& Y& (X-\overline{X})& (Y-\overline{Y})& (X-\overline{X}{)}^2& (Y-\overline{Y}{)}^2\\ 35& 108& -16& 3& 256& 9\\ 54& 107& 3& 2& 9& 4\\ 52& 105& 1& 0& 1& 0\\ 53& 105& 2& 0& 4& 0\\ 56& 106& 5& 1& 25& 1\\ 58& 107& 7& 2& 49& 4\\ 52& 104& 1& -1& 1& 1\\ 50& 103& -1& -2& 1& 4\\ 51& 104& 0& -1& 0& 1\\ 49& 101& -2& -4& 4& 16\\ 510& 1050& & & 350& 40\end{array}$

$\left(\overline{x}\right)$ = $\frac{510}{10}=51,\left(\overline{y}\right)=\frac{1050}{10}=105$

${\sigma }_x=\sqrt{\frac{\sum (x-\overline{x}{)}^2}{n}}=\sqrt{\frac{350}{10}}=5.92$

${\sigma }_y=\sqrt{\frac{\sum (x-\overline{y}{)}^2}{n}}=\sqrt{\frac{40}{10}}=2$

$\text{C.V. of}x=\frac{5.92}{51}\times 100=11.61$

$\text{C.V. of}y=\frac{2}{105}\times 100=1.9$

$\text{C.V. or}Y<\text{C.V. of}X$

Thus prices of share Y are more stable.