Question

The mean score of 25 observations is 80 and the mean score of another 55 observations is 60. Determine the mean score of the whole set of observations.

Answer 1

Mean score of 25 observations = 80
Sum of the scores of 25 observations = 80$\times$25 = 2000
Mean score of another 55 observations = 60
Sum of the scores of another 55 observations = 60$\times$55 = 3300

$\mathrm{Mean}\mathrm{score}\mathrm{of}\mathrm{the}\mathrm{whole}\mathrm{set}\mathrm{of}\mathrm{observations}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{scores}\mathrm{of}25\mathrm{observations}+\mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{scores}\mathrm{of}\mathrm{another}55\mathrm{observations}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{observations}}$

$$\begin{gathered} =\frac{2000+3300}{80} \\ =\frac{5300}{80} \\ =66.25 \end{gathered}$$

Therefore, the mean score of the whole set of observations is 66.25.