From the data given below state which group is more variable A or B?

Toolbox:
• The formula required to solve this problem are : Mean $A+ \large\frac{\sum f_i d_i}{\sum f_i} $$\times h • Standard deviation \sigma= \sqrt {\large\frac{\sum f_i d_i^2}{\sum f_i} - \bigg( \large\frac{\sum f_i d_i}{\sum f_i} \bigg)^2 }$$ \times h$
• Coefficient variation $=\large\frac{\sigma}{\bar {x} }$$\times 100 For Group A: Step 1: h=10 A=As \;n\;is \;odd \qquad= \bigg( \large\frac{n+1}{2}\bigg)^{th} observation \qquad= \bigg( \large\frac{7+1}{2}\bigg)^{th} observation \qquad= 4th observation \qquad=45 A=45 Step 2: Mean A+ \large\frac{\sum f_i d_i}{\sum f_i}$$ \times h$
$\qquad= A+ \large\frac{(-6)}{150} $$\times 10 \qquad= 45 - \large\frac{6}{15} \qquad= 45-0.4=44.6 Step 3: Standard deviation \sigma= \sqrt {\large\frac{\sum f_i d_i^2}{\sum f_i} - \bigg( \large\frac{\sum f_i d_i}{\sum f_i} \bigg)^2 }$$ \times h$
$\qquad= \sqrt {\large\frac{342}{150} - \bigg(\large\frac{-6}{150} \bigg)^2} $$\times10 \qquad= \large\frac{10}{150}$$ \sqrt {51300 -36}$
$\qquad= \large\frac{1}{15} $$\sqrt {51264} \qquad= 15.09 Step 4: Coefficient variation =\large\frac{\sigma}{\bar {x} }$$ \times 100$
$\qquad= \large\frac{15.09}{44.6} $$\times 100 \qquad= \large\frac{1509}{44.6} \qquad= 33.83 \therefore For Group A, Mean =44.6, \sigma=15.09 CV= 33.83 For Group B: Step 1: h=10 A=45(as in group A) Step 2: Mean A+ \large\frac{\sum f_i d_i}{\sum f_i}$$ \times h$
$\qquad= 45+ \large\frac{(-6)}{150} $$\times 10 << Enter Text >>\qquad= 45-0.4=44.6 Step 3: Standard deviation \sigma= \sqrt {\large\frac{\sum f_i d_i^2}{\sum f_i} - \bigg( \large\frac{\sum f_i d_i}{\sum f_i} \bigg)^2 }$$ \times h$
$\qquad= \sqrt {\large\frac{366}{150} - \bigg(\large\frac{-6}{150} \bigg)^2} $$\times10 \qquad= \large\frac{10}{150}$$ \sqrt {54900 -36}$
$\qquad= \large\frac{1}{15} $$\sqrt {54864} \qquad= 15.61 Step 4: Coefficient variation =\large\frac{\sigma}{\bar {x} }$$ \times 100$
$\qquad= \large\frac{15.61}{44.6}$$\times 100$
$\qquad= \large\frac{1561}{44.6}$
$\qquad=35$
COMPARISON:
The group which has the higher coefficient variation will be more variable.
Therefore Group B Coefficient variation is greater as compared to group A coefficient variation.
$\therefore$ Group B is more variable.