Question

The following is the record of goals scored by team A in a football session :

$\begin{array}{cccccc}\text{No. of goals scored}& 0& 1& 2& 3& 4\\ \text{No. of matches}& 1& 9& 7& 5& 3\end{array}$

For the 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 ?

Answer 1

Team A

$\begin{array}{cccc}{x}_i& f_i& f_i{x}_i& f{x}^2\\ 0& 1& 0& 0\\ 1& 9& 9& 9\\ 2& 7& 14& 28\\ 3& 5& 15& 45\\ 4& 3& 12& 48\\ & 25& 50& 130\end{array}$

$\text{Mean}\left(\overline{x_A}\right)=\frac{1}{N}\sum fx=\frac{1}{25}\times 50=2$

$\text{S.D.}\left({\sigma }_A\right)=\sqrt{\frac{\sum f{x}^2}{N}-{\left(\frac{\sum fx}{N}\right)}^2}$

$=\sqrt{\frac{130}{25}-{\left(\frac{50}{25}\right)}^2}$

$=\sqrt{5.2-4}=\sqrt{1.2}=1.09$

$\therefore \text{C.V. of team A}=\frac{1.09}{2}\times 100=54.5$

$\text{C.V. of team B}=\frac{1.25}{2}\times 100=62.5$

$\text{Since C.V. of team A}<\text{C.V. of team B}.\text{Thus team A is more consistent.}$