Question

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

X:	35	54	52	53	56	58	52	50	51	49
Y:	108	107	105	105	106	107	104	103	104	101

Answer 1

Let A_x = 51

$x_i$	$d_i=x_i-51$	${d_i}^2$
35	$-$16	256
54	3	9
52	1	1
53	2	4
56	5	25
58	7	49
52	1	1
50	$-$1	1
51	0	0
49	$-$2	4
	$\sum d_i=0$	$\sum {d_i}^2=350$

Here, we have
$$\begin{gathered} n=10,\overline{X}=51 \\ {\sigma }^2=\frac{\sum {d_i}^2}{n}-{\left(\frac{\sum d_i}{n}\right)}^2 \\ =\frac{350}{10}-{\left(\frac{0}{10}\right)}^2 \\ =35-0 \\ =35 \end{gathered}$$

$\sigma =\sqrt{35}=5.91$

$$\begin{gathered} {\mathrm{CV}}_x=\frac{5.91}{51}\times 100 \\ =11.58 \end{gathered}$$

Let A_y =105

$x_i$	$d_i=x_i-105$	${d_i}^2$
108	3	9
107	2	4
105	0	0
105	0	0
106	1	1
107	2	4
104	$-$1	1
103	$-$2	4
104	$-$1	1
101	$-$4	16
	$\sum d_i=0$	$\sum {d_i}^2=40$

$$\begin{gathered} n=10,\overline{Y}=105 \\ {\sigma }^2=\frac{\sum {d_i}^2}{n}-{\left(\frac{\sum d_i}{n}\right)}^2 \\ =\frac{40}{10}-{\left(\frac{0}{10}\right)}^2 \\ =4-0 \\ =4 \end{gathered}$$

$\sigma =\sqrt{4}=2$

$$\begin{gathered} {\mathrm{CV}}_y=\frac{2}{105}\times 100 \\ =1.90 \end{gathered}$$

Since CV of prices of share Y is lesser than that of X, prices of shares Y are more stable.