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Home  >>  CBSE XI  >>  Math  >>  Statistics
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The following is the record of goals scored by team A in a football session. For Team B , mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent ?

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Toolbox:
  • The formula required to solve this problem are : Mean $ A+ \large\frac{\sum f_i x_i}{\sum f_i} $
  • Standard deviation $\sigma= \sqrt {\large\frac{\sum f_i x_i^2}{\sum f_i} - \bigg( \large\frac{\sum f_ix_i}{\sum f_i} \bigg)^2 }$$ \times h$
  • Coefficient variation $=\large\frac{\sigma}{\bar {x} }$$ \times 100$
Step 2:
For Team A: : Mean $ A+ \large\frac{\sum f_i x_i}{\sum f_i} $
$\qquad= \large\frac{50}{25}$
$\qquad= 2$
Step 3:
Standard deviation $\sigma= \sqrt {\large\frac{\sum f_i x_i^2}{\sum f_i} - \bigg( \large\frac{\sum f_ix_i}{\sum f_i} \bigg)^2 }$$ \times h$
$\qquad= \sqrt { \large\frac{130}{25} - \bigg( \large\frac{50}{25}\bigg)^2}$
$\qquad= \sqrt{\large\frac {30}{25}}$
$\qquad= \large\frac{5.48}{5} $$=1.096$
Step 4:
Coefficient variation $=\large\frac{\sigma}{\bar {x} }$$ \times 100$
$\qquad= \large\frac{1.096 }{2}$$ \times 100$
$\qquad= \large\frac{109.6}{2}$
$\qquad=54.8$
For team B:
Mean $\bar {X} =2$(given)
$\sigma= 1.25$ (given)
Step 1:
Coefficient variation $=\large\frac{\sigma}{\bar {x} }$$ \times 100$
$\qquad= \large\frac{1.25}{2} $$\times 100$
$\qquad= \large\frac{125}{2}$
$\qquad= 62.5$
COMPARISON:
Consistency of the team depends upon the coefficient of variation.
Lesser the coefficient of variation, more consistent the team is
$\therefore $ coefficient of variation team A is lesser as compared to coefficient of variation of team B.
Team A is more consistent.
answered Jul 1, 2014 by meena.p
 

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