The average marks of a student in 4 subjects is 75. If the student obtained 80 marks in the fifth subject, then the new average is

### Concept & Formula The average is calculated as the sum of all observations divided by the number of observations. $$Average = \frac{Sum \ of \ Observations}{Number \ of \ Observations}$$ When a new observation is added, we find the new sum and divide by the new total count. ### Step-by-Step Solution * **Initial Total:** The average of 4 subjects is 75. $$Total \ marks \ (4 \ subjects) = 4 \times 75 = 300$$ * **New Total:** The student gets 80 marks in the 5th subject. $$Total \ marks \ (5 \ subjects) = 300 + 80 = 380$$ * **New Average:** Divide the new total by 5 subjects. $$New \ Average = \frac{380}{5} = 76$$ ### Exam Strategy & Shortcut Use the **Deviation Method** to solve this mentally. The old average is 75. The new subject score is 80, which is $+5$ above the average. Distribute this surplus of 5 marks equally among all 5 subjects: $$\frac{+5}{5} = +1$$ Add this distributed surplus to the old average: $$New \ Average = 75 + 1 = 76$$ ### Common Pitfall A frequent error is dividing the new total sum (380) by the old number of subjects (4), which yields 95, or simply averaging the old average and the new score: $\frac{75+80}{2} = 77.5$. Always remember to update the denominator to reflect the new total count. ### Final Answer Therefore, the correct answer is 76.