The mean amount of time that the 20 employees of a construction company have worked for the company is 6.7...

1. TRANSLATE the problem information

• Given information:
  • 20 employees initially with mean of 6.7 years
  • After one employee leaves: 19 employees with mean of 6.25 years
  • Need to find: years worked by the employee who left

• What this tells us: We can use the relationship between mean, total, and count to find the missing value

2. INFER the solution strategy

• Key insight: If we know the total years before and after the employee left, the difference gives us that employee's years
• Strategy: Calculate total years for both scenarios, then subtract

3. SIMPLIFY to find the initial total

• Total years for 20 employees = \(20 \times 6.7 = 134\) years

4. SIMPLIFY to find the remaining total

• Total years for 19 remaining employees = \(19 \times 6.25 = 118.75\) years
  (Use calculator for this decimal multiplication)

5. SIMPLIFY to find the leaving employee's years

• Years worked by leaving employee = \(134 - 118.75 = 15.25\) years

Answer: D. 15.25

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students calculate the difference in means (\(6.7 - 6.25 = 0.45\)) and think this represents the leaving employee's years worked.

This fundamental misunderstanding of what the mean difference represents versus what the problem is actually asking leads them to select Choice A (0.45).

Second Most Common Error Path:

Weak INFER reasoning: Students correctly calculate totals but make strategic errors in their approach - such as assuming there are still 20 employees after someone left, leading to calculations like \(20 \times 6.25 = 125\), then \(134 - 125 = 9.00\).

This flawed reasoning about the number of remaining employees leads them to select Choice C (9.00).

The Bottom Line:

This problem tests whether students truly understand the relationship between individual values, totals, and means - not just the formula itself, but how to use that relationship strategically to work backwards from means to find individual contributions.