Study the following table carefully and answer the question given below. It…

Concept: The average of a group of values is (sum of values) ÷ (count of values). When a question asks for the sum of two DIFFERENT groups' averages, the reliable general method is to compute each group's average separately and then add the two averages — this always works, whatever the two group sizes are. (Only when both groups happen to have the SAME count — as here, five factories in each shift — does adding the raw sums first and dividing once by that shared count give the identical result; that shortcut breaks down the moment the group sizes differ, so the separate-then-add method is the one to rely on.)

1. From the table, the number of workers (in thousands) during the 7 A.M.–11 A.M. shift for the five factories is 7.5, 8, 7.8, 7.59 and 8.32.

2. Sum these five values: 7.5 + 8 + 7.8 + 7.59 + 8.32 = 39.21 (thousand); scaling by 1000 gives a total of 39210 workers.

3. Divide by the 5 factories to get the average for the morning shift: 39210 ÷ 5 = 7842.

4. For the 7 P.M.–11 P.M. shift, the five factory values (in thousands) are 7.8, 5.25, 6, 6 and 6.5.

5. Sum these five values: 7.8 + 5.25 + 6 + 6 + 6.5 = 31.55 (thousand); scaling by 1000 gives a total of 31550 workers.

6. Divide by the 5 factories to get the average for the evening shift: 31550 ÷ 5 = 6310.

7. Add the two shift averages: 7842 + 6310 = 14152.

Cross-check: Both shift averages fall between 6000 and 8000 workers, so their sum should lie between 12000 and 16000 — this rules out a total as low as 11502, while independently recomputing 39210 ÷ 5 and 31550 ÷ 5 and adding again reproduces the same 14152.