The average marks of 100 students are given to be 40. It was found later that marks of one student were 53 which were misread as 83. The corrected mean marks are
Answer & explanation
Answer: (b) 39.7
The total was overstated by 83 − 53 = 30 marks, so the correct total is 3970 and the mean is 39.7.
- Recorded total = 100 × 40 = 4000.
- Excess from the misreading = 83 − 53 = 30.
- Correct total = 4000 − 30 = 3970; correct mean = 3970/100 = 39.7.
- Shortcut: the mean falls by 30/100 = 0.3.
Remember · One wrong entry shifts the mean by (wrong − right) ÷ n.
Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·