# From the prices of shares A and Y below. Find out which is more stable in value.

Toolbox:
• The formula required to solve this problem are : Mean $A+ \large\frac{\sum f_i d_i}{\sum f_i} $$\times h • Standard deviation \sigma= \sqrt {\large\frac{\sum d_i^2}{n} - \bigg( \large\frac{\sum d_i^2}{n} \bigg)^2 }$$ \times h$
• Coefficient variation $=\large\frac{\sigma}{\bar {x} }$$\times 100 Step 1: Let Assumed mean A=52 for share X Step 2: Mean = A+ \large\frac{\sum d_i}{n} \qquad= 52 +\large\frac{(-10)}{10} \qquad= 52-1 \qquad= 51 Step 3: Standard deviation \sigma= \sqrt {\large\frac{\sum d_i^2}{n} - \bigg( \large\frac{\sum d_i^2}{n} \bigg)^2 } \qquad= \sqrt { \large\frac{360}{10} - \bigg( \large\frac{-10}{10}\bigg)^2} \qquad= \sqrt {36-1} \qquad= \sqrt {35} \qquad= 5.92 Step 4: Coefficient variation =\large\frac{\sigma}{\bar {x} }$$ \times 100$
$\qquad= \large\frac{5.92}{51}$$\times 100 \qquad= \large\frac{592}{51}$$=11.60$
For share y, Let Assumed mean $A=105$
Step 1:
Step 2:
Mean =$A+ \large\frac{\sum d_2}{n}$
$\qquad= 105 +\large\frac{0}{10}$
$\qquad=105$
Step 3:
Standard deviation $\sigma= \sqrt {\large\frac{\sum d_i^2}{n} - \bigg( \large\frac{\sum d_i^2}{n} \bigg)^2 }$
$\qquad= \sqrt {\large\frac{40}{10 } -\bigg(\frac{0}{10}\bigg)^2}$
$\qquad= \sqrt {4}$
$\qquad=2$
Step 4:
Coefficient variation $=\large\frac{\sigma}{\bar {x} }$$\times 100 \qquad=\large\frac{2}{105}$$ \times 100$
$\qquad= \large\frac{200}{105}$
$\qquad= 1.90$
COMPARISON:
Shares, whose coefficient variation is lesser is considered to be more stable.
$\therefore$ CV of share Y is lesser as compared to CV of share X.
$\therefore$ Share Y is more stable.