If $k$ sets of data consist, respectively, of $n_{1}, n_{2}, \ldots, n_{k}$ observations and have the means $\bar{x}_{1}, \bar{x}_{2}, \ldots, \bar{x}_{k}$, then the overall mean of all the data is given by the formula

\[\bar{x}=\frac{\sum_{i=1}^{k} n_{i} \bar{x}_{i}}{\sum_{i=1}^{k} n_{i}}\]

(a) There are 15 students in semester I, 25 students in semester II and 16 students in semester III in an engineering program. If the average attendance of students is 82,74 , and 79 in semesters I, II and III respectively, what is the mean for the entire program?

(b) The average monthly expenses on repairs of machines in four factories are $\$ 1,800, \$ 4,200$, $\$ 12,000$ and $\$ 800$. If the number of machines in these factories is $12,18,42$, and 8 respectively, find the average amount spent on repairs of these 80 machines.