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Home  >>  CBSE XI  >>  Math  >>  Statistics
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From the data given below state which group is more variable A or B?

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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.
answered Jun 30, 2014 by meena.p
 

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