Solve 9

Q 9    Calculate S. D. and coefficient of variation 

Dear Tushar,
Using the Assumed Mean Method, we can find the standard deviation as follows:
 

X	f	m	d	fd	d2	fd2
117.5-126.5	3	122	–18	– 54	324	972
126.5-135.5	5	131	–9	–45	81	405
135.5-144.5	9	140=A	0	0	0	0
144.5-153.5	12	149	9	108	81	972
153.5-162.5	5	158	18	90	324	1620
162.5-171.5	4	167	27	108	729	2916
171.5-180.5	2	176	36	72	1296	2592

$$\begin{gathered} S.D=\sqrt{\frac{\sum _{ }f{d}^2}{\sum _{ }f}-{\left({\displaystyle \frac{\sum _{ }fd}{\sum _{ }f}}\right)}^2} \\ S.D=\sqrt{\frac{9477}{40}-{\left({\displaystyle \frac{279}{40}}\right)}^2} \\ S.D=\sqrt{236.925-48.650} \\ S.D=\sqrt{188.275} \\ S.D=13.72 \end{gathered}$$

Also, 
$\text{Coefficient of }Variance=\frac{\text{Standard Deviation}}{\text{Mean}}\times 100$
So, using the formula, you can find the CV accordingly. In case you still face any problem, let us know.