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Difficulty: EasyWeighted Average and Combined Sets

A technology firm consists of two divisions: Division X and Division Y. Division X has 2020 employees with an average monthly salary of $5000\$5{}000, while Division Y has 3030 employees with an average monthly salary of $6000\$6{}000. What is the average monthly salary of all 5050 employees combined?

  1. A
    $5400\$5{}400
  2. B
    $5500\$5{}500
  3. $5600\$5{}600Answer
  4. D
    $5700\$5{}700
  5. E
    $5800\$5{}800

Answer

The combined average monthly salary for all 5050 employees is $5600\$5{}600.
The total salary for Division X is 20×$5000=$10000020 \times \$5{}000 = \$100{}000 and for Division Y is 30×$6000=$18000030 \times \$6{}000 = \$180{}000. Combining both gives a total payout of $280000\$280{}000 across 5050 employees. Dividing $280000\$280{}000 by 5050 yields an exact weighted average of $5600\$5{}600.

Step-by-Step Solution

1
Calculate total monthly salary expenditure for Division X
20×$5000=$10000020 \times \$5{}000 = \$100{}000
Total value of a set equals the number of items times the average value per item.
2
Calculate total monthly salary expenditure for Division Y
30×$6000=$18000030 \times \$6{}000 = \$180{}000
Total value of a set equals the number of items times the average value per item.
3
Sum total monthly salary expenditures and total number of employees
Total salary = $100000+$180000=$280000\$100{}000 + \$180{}000 = \$280{}000; Total employees = 20+30=5020 + 30 = 50
Combined set averages require combined total sum divided by combined total quantity.
4
Compute the combined weighted average salary
$28000050=$5600\frac{\$280{}000}{50} = \$5{}600
Weighted average formula: Weighted Average=Total SumTotal Count\text{Weighted Average} = \frac{\text{Total Sum}}{\text{Total Count}}.

Key Concept

Weighted Average of Combined Sets
Estimated Time:1m 0s
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Topics

Weighted Average and Combined Sets

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