Question

The number of goals scored by two teams in a football session were as under:

$\begin{array}{ccccccc}\text{No of goals scored}& 0& 1& 2& 3& 4& 5\\ \text{No of matches (Team A)}& 15& 10& 7& 5& 3& 2\\ \text{No of matches (Team B)}& 20& 10& 5& 4& 2& 1\end{array}$

Which team is more consistent?

Answer 1

$\begin{array}{cccccc}\left(X_A\right)& \text{Team A}& X_A^2& \left(X_B\right)& \text{Team B}& X_B^2\\ & X_A-\overline{X}\left(X_A\right)& & & X_B-\overline{X}\left(X_B\right)& \\ 15& 8& 64& 20& 13& 169\\ 10& 3& 9& 10& 3& 9\\ 7& 0& 0& 5& -2& 4\\ 5& -2& 4& 4& -3& 9\\ 3& -4& 16& 2& -5& 25\\ 2& -5& 25& 1& -6& 36\\ \sum =42& & \sum =118& \sum =42& & \sum =252\end{array}$

$\begin{array}{cc}\text{Team}& \text{Team B}\\ X_A=\frac{\sum X_A}{N}=\frac{42}{6}=7& X_B=\frac{\sum X_B}{N}=\frac{42}{6}=7\\ {\sigma }_A=\sqrt{\frac{\sum X_A^2}{N}}=\sqrt{\frac{118}{6}}=4.43& {\sigma }_B=\sqrt{\frac{\sum X_B^2}{N}}=\sqrt{\frac{252}{6}}=6.48\\ \text{C.V.(Team A)}=\frac{\sigma }{X_A}\times 100& \text{C.V.(Team B)}=\frac{\sigma }{X_B}\times 100\\ =\frac{4.43}{7}\times 100=63.29\%& =\frac{6.48}{7}\times 100=92.57\%\end{array}$

C.V. of Team A is less than C.V. of Team B, so Team A is more consistent.