Question

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

$\begin{array}{cccccc}No.ofgoalsscored& 0& 1& 2& 3& 4\\ No.ofmatches& 1& 9& 7& 5& 3\end{array}$

For the team B, mean number of goals scored per match was 2 with standard deviation 1.25 goals. Find which team may be considered more consistent?

Answer 1

Team A

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

Mean, $\left(\overline{x_a}\right)=\frac{\sum fx}{N}=50/25=2.$
Standard deviation$\left({\sigma }_A\right)=\sqrt{\frac{\sum f{x}^2}{N}-(\frac{\sum fx}{N}{)}^2}=\sqrt{\frac{130}{25}-(\frac{50}{25}{)}^2}=\sqrt{5.2-4}=\sqrt{1.2}=1.09$

C.V of team A = (1.09/2) $\times$ 100 = 54.5 and

C.V of team B = (1.25/2) $\times$ 100 = 62.5

Here, C.V of team A < C.V of team B

Therefore, team A is more consistent.