Study the following table carefully and answer the questions given below.…
2024
Study the following table carefully and answer the questions given below. Number of workers in the given six shifts of various factories (numbers in thousands).
What is the total of the average number of workers working in the shift of 7 A.M. to 11 A.M. from all the factories and the average number of workers working in the shift of 7 P.M. to 11 P.M. from all the factories? [Questions 25 to 30 are based on this table.]
- A.
11502
- B.
15142
- C.
14520
- D.
14152
Show answer & explanation
Correct answer: D
Concept: The average of a set of values is (sum of the values) ÷ (number of values). When two different groups (here, two separate shifts) each have their own average, the combined total of the two averages is found by computing each group's average separately first, and then adding the two resulting averages — not by combining the raw sums before dividing.
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.
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.
Divide by the 5 factories to get the average for the morning shift: 39210 ÷ 5 = 7842.
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.
Sum these five values: 7.8 + 5.25 + 6 + 6 + 6.5 = 31.55 (thousand); scaling by 1000 gives a total of 31550 workers.
Divide by the 5 factories to get the average for the evening shift: 31550 ÷ 5 = 6310.
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.