Consider the table given below and answer the following questions given below.…

Concept: When only some values in a set change by different percentages, you cannot adjust the old average directly. Revise the running total for each subgroup using its own percentage change, combine the revised subgroup totals into one new grand total, and divide by the original number of items — the count of items stays the same, only the values change.

Application: From the table, the number of books published is A = 28,200; B = 32,200; C = 29,700; D = 31,200; E = 33,800; F = 35,700; G = 37,800 — seven publishing houses in all.

1. Sum of D, E and F = 31,200 + 33,800 + 35,700 = 1,00,700 books.

2. Raise this sum by 20%: 1,00,700 × 1.2 = 1,20,840 books.

3. Sum of the remaining publishers A, B, C and G = 28,200 + 32,200 + 29,700 + 37,800 = 1,27,900 books.

4. Lower this sum by 20%: 1,27,900 × 0.8 = 1,02,320 books.

5. New grand total for all seven publishers = 1,20,840 + 1,02,320 = 2,23,160 books.

6. New average = 2,23,160 ÷ 7 = 31,880 books.

Cross-check: The original grand total was 28,200 + 32,200 + 29,700 + 31,200 + 33,800 + 35,700 + 37,800 = 2,28,600, an original average of about 32,657. The net change in the grand total is (20% of 1,00,700) − (20% of 1,27,900) = 20,140 − 25,580 = −5,440, so the new total is 2,28,600 − 5,440 = 2,23,160 — matching the total obtained above and confirming the new average.

Hence, the new average number of books published by all seven publishers is 31,880.