Question

From the prices of shares $X$ and $Y$ 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

$X_i$	$|X_i-\overline{X}|$	$|X_i-\overline{X}{|}^2$
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
Total= 510

Here, the number of observations $n=10$
$\therefore Mean,\overline{X}=\frac{1}{n}\sum _{i=1}^{10}{X}_i=\frac{1}{10}\times 510=51$

Variance$\left({\sigma }_1^2\right)=\frac{1}{n}\sum _{i=1}^{10}(X_i-\overline{X}{)}^2$

$=\frac{1}{10}\times 350=35$
$\therefore$ Standard deviation $\left({\sigma }_1\right)=\sqrt{35}=5.91$

$Y_i$	$|Y_i-\overline{Y}|$	$|Y_i-\overline{Y}{|}^2$
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
Total= 1050		40

Here, the number of observations $n=10$
$\therefore Mean,\overline{Y}=\frac{1}{n}\sum _{i=1}^{10}{Y}_i=\frac{1}{10}\times 1050=105$

Variance$\left({\sigma }_2^2\right)=\frac{1}{n}\sum _{i=1}^{10}(Y_i-\overline{Y}{)}^2$

$=\frac{1}{10}\times 40=4$
$\therefore$ Standard deviation $\left({\sigma }_2\right)=\sqrt{4}=2$

Since, the variance of prices of share $X$ is greater than that of prices of share $Y$.

So, prices of share $X$ are more variable than prices of share $Y$.

So, the prices of shares $Y$ are more stable than the prices of share $X$.