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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 ?

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.