Average salary of 15 employees — which statements suffice? I. Average salary of 7 clerical employees is $8,500. II. Average salary of 5 officer employees is $10,000. III. Average salary of 3 sub-staff employees is $2,500.
Correct Answer: All I, II and III together
Introduction / Context:The task is to decide which statements are sufficient to compute the overall average salary of 15 employees, given subgroup averages and subgroup sizes.
Given Data / Assumptions:
- Total headcount = 15 (7 clerical, 5 officers, 3 sub-staff).
- I: Average of 7 clerical = $8,500.
- II: Average of 5 officers = $10,000.
- III: Average of 3 sub-staff = $2,500.
Concept / Approach:The combined average is a weighted mean: (Σ subgroup_total) / 15, where each subgroup_total = (subgroup_avg * subgroup_count). To compute the overall average uniquely, we need all subgroup totals (or an equivalent).
Step-by-Step Solution:
From I: total clerical pay = 7 * 8,500 = 59,500.From II: total officer pay = 5 * 10,000 = 50,000.From III: total sub-staff pay = 3 * 2,500 = 7,500.Grand total = 59,500 + 50,000 + 7,500 = 117,000.Overall average = 117,000 / 15 = $7,800.Verification / Alternative check:Missing any one subgroup leaves an unknown portion of the total, preventing a unique overall average.
Why Other Options Are Wrong:
- Only I / Only II / Only III: Insufficient; partial data.
- Any two: Still leaves the third subgroup unknown.
Common Pitfalls:Assuming the remaining subgroup can be deduced; it cannot without additional constraints.
Final Answer:All I, II and III together