Question

Ten players of the Australian team made an average of 63 runs and ten players of the Indian team made an average of 77 runs. Calculate the average run made by both the teams.

Answer 1

The information given in the question can be summarised as follows.

	Average Runs	Number of Players
Australian Team	$\left({\overline{X}}_1\right)$ = 63	N1 = 10
Indian Team	$\left({\overline{X}}_2\right)$ = 77	N1 = 10

The combined average is calculated using the following formula.
$$\begin{gathered} {\overline{X}}_{12}=\frac{N_1{\overline{X}}_1+N_2{\overline{X}}_2}{N_1+N_2} \\ \mathrm{Substituting}\mathrm{the}\mathrm{given}\mathrm{values}\mathrm{in}\mathrm{the}\mathrm{formula}. \\ {\overline{X}}_{12}=\frac{10\times 63+10\times 77}{10+10} \\ =\frac{1400}{20}=70 \end{gathered}$$
Hence, the average scored by both the teams is 70.