Question

Goals scored by two teams A and B in football matches were as follows:

No. of Goals in a match	:	0	1	2	3	4
No.of Matches: A	:	27	9	8	5	4
B	:	17	9	6	5	3

Find the team which is more consistent in its performance.

Answer 1

For Team A

X	f	fX	Deviation from mean ${\mathit{x}}_{\mathbf{A}}\mathbf{=}\left(\mathit{X}\mathbf{-}{\overline{\mathit{X}}}_{\mathbf{A}}\right)$	${\mathit{x}}_{\mathbf{A}}^{\mathbf{2}}$	$\mathit{f}{\mathit{x}}_{\mathbf{A}}^{\mathbf{2}}$
0 1 2 3 4	27 9 8 5 4	0 9 16 15 16	−1.06 −0.06 0.94 1.94 2.94	1.12 0.0036 0.88 3.76 8.64	30.24 0.03 7.04 18.8 34.56
	Σf = 53	ΣfX = 56			$\mathrm{\Sigma }f{x}_{\mathrm{A}}^2=90.68$

$$\begin{gathered} {\overline{X}}_{\mathrm{A}}=\frac{\mathrm{\Sigma }fX}{\mathrm{\Sigma }f}=\frac{56}{53}=1.06 \\ S{D}_{\mathrm{A}}=\sqrt{\frac{\mathrm{\Sigma }f{x}_{\mathrm{A}}^2}{\mathrm{\Sigma }f}}=\sqrt{\frac{90.68}{53}}=\sqrt{1.71} \\ =1.31 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{variation}=\frac{S{D}_{\mathrm{A}}}{{\overline{X}}_{\mathrm{A}}}\times 100=\frac{1.31}{1.06}\times 100=123.6\% \end{gathered}$$

For Team B

X	f	fX	Deviation from mean ${\mathit{x}}_{\mathbf{B}}\mathbf{=}\left(\mathit{X}\mathbf{-}{\overline{\mathit{X}}}_{\mathbf{B}}\right)$	${\mathit{x}}_{\mathbf{B}}^{\mathbf{2}}$	$\mathit{f}{\mathit{x}}_{\mathbf{B}}^{\mathbf{2}}$
0 1 2 3 4	17 9 6 5 3	0 9 12 15 12	−1.2 −0.2 0.8 1.8 2.8	1.44 0.04 0.64 3.24 7.84	24.48 0.36 3.84 16.2 23.52
	Σf = 40	ΣfX= 48			$\mathrm{\Sigma }f{x}_{\mathrm{B}}^2=68.4$

$$\begin{gathered} {\overline{\mathit{X}}}_{\mathrm{B}}=\frac{\mathrm{\Sigma }fX}{\mathrm{\Sigma }f}=\frac{48}{40}=1.2 \\ S{D}_{\mathrm{B}}=\sqrt{\frac{\mathrm{\Sigma }f{x}_{\mathrm{B}}^2}{\mathrm{\Sigma }f}}=\frac{68.4}{40}=\sqrt{1.71}=1.31 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{variation}=\frac{S{D}_{\mathrm{B}}}{{\overline{\mathit{X}}}_{\mathrm{B}}}\times 100 \\ =\frac{1.31}{1.2}\times 100=109.1\% \end{gathered}$$
Since, coefficient of variation is lesser for team B, it is more consistent.