What is the average of the total number of employees in the Accounts, HR,…

Concept — In a percentage-distribution table every share is measured against one and the same total. So if any single department's actual strength and its percentage share are both known, one percentage point is worth strength divided by percentage, and every other department's strength is that unit value multiplied by its own percentage. The average of k departments is then the sum of their strengths divided by k.

Application

1. Marketing carries 14% of the workforce and that equals 560 employees, so 1% is worth 560 divided by 14, that is 40 employees.

2. The whole workforce is therefore 100 times 40, that is 4,000 employees.

3. The four departments named in the question carry 18% (Accounts), 12% (HR), 14% (Marketing) and 32% (Production), a combined share of 18 + 12 + 14 + 32 = 76%.

4. Their combined strength is 76 times 40, that is 3,040 employees.

5. Averaging that combined strength over the four departments gives 3,040 divided by 4, that is 760 employees.

Cross-check

Computing each of the four departments separately from the unit value 1% = 40 employees gives the same combined strength:

The table total 3,040 divided by 4 is again 760, so both routes agree. As a further sanity check, the six listed shares add up to 8 + 18 + 12 + 14 + 32 + 16 = 100%, confirming that the table is a complete distribution and that the unit value 1% = 40 employees holds throughout.

Result — The average strength of the Accounts, HR, Marketing and Production departments is 760 employees.