Five salaries are Rs. 8000, Rs. 5000, Rs. 11000, Rs. 7000, and Rs. 9000 per month. What is the average monthly salary?
Correct Answer: Rs. 8000
Introduction / Context:Average salary problems are straightforward applications of the arithmetic mean. Careful summation ensures accuracy when some values are above and some below the final average.
Given Data / Assumptions:
- Salaries (per month): 8000, 5000, 11000, 7000, 9000 (in rupees)
- Number of people: 5
Concept / Approach:Average = (sum of all salaries) / 5. Adding in balanced pairs reduces addition mistakes.
Step-by-Step Solution:
Sum = 8000 + 5000 + 11000 + 7000 + 9000 Compute pairs: (8000 + 7000) = 15000; (5000 + 11000) = 16000; remaining 9000 Total sum = 15000 + 16000 + 9000 = 40000 Average = 40000 / 5 = Rs. 8000Verification / Alternative check:Check spread around 8000: values are 5000 (−3000), 7000 (−1000), 8000 (0), 9000 (+1000), 11000 (+3000). Offsets sum to zero, confirming 8000 is the mean.
Why Other Options Are Wrong:
- Rs. 7000 and Rs. 9000: Too low/high relative to balanced offsets.
- Rs. 8500: Not supported by the exact arithmetic; suggests rounding error.
- None of these: A correct exact value exists.
Common Pitfalls:Arithmetic slips when several terms require addition; forgetting to divide by the correct count of individuals.
Final Answer:Rs. 8000