The average weight of a group of 75 girls was calculated as 47 kgs. It was later discovered that the weight of one of the girls was read as 45 kgs. Whereas her actual weight was 25 kgs. What is the actual average weight of the group of 75 girls? (Rounded off to two digits after decimal)

### Concept & Formula When a data point is incorrectly recorded in an average calculation, we do not need to recalculate the entire sum from scratch. We only need to find the net change (error) and distribute that change equally across the total number of observations. $$\text{Correction in Average} = \frac{\text{Actual Value} - \text{Incorrect Value}}{\text{Total Number of Observations}}$$ $$\text{New Average} = \text{Old Average} + \text{Correction}$$ ### Step-by-Step Solution * **Given Data:** Number of girls ($N$) = 75 Old Average = 47 kg Incorrect recorded weight = 45 kg Actual correct weight = 25 kg * **Calculate the Net Error:** The person's weight was recorded as 45 kg, but it should have only been 25 kg. This means the original sum was artificially inflated. Net Change = Actual - Incorrect Net Change = $25 - 45 = -20$ kg. (The total sum needs to decrease by 20 kg). * **Calculate the Average Correction:** Distribute this $-20$ kg change across all 75 girls to see how it affects the average. Change in Average = $\frac{-20}{75}$ Change in Average = $\frac{-4}{15}$ Change in Average $\approx -0.266...$ kg. * **Calculate New Average:** New Average = $47 - 0.266$ New Average = $46.73$ kg (rounded to two decimal places). * **Evaluate Options:** The calculated actual average is 46.73 kg. The provided options are (a) 34, (b) 36, (c) 30. None of these options are even close to the correct value. ### Exam Strategy & Shortcut Use the Deviation Method instantly. You see an over-calculation of 20 kg ($45 - 25 = 20$). This means the real average must be slightly *less* than 47. How much less? $\frac{20}{75}$, which is a tiny fraction (less than 1). So the real average is around 46.7. Look at the options: 34, 36, 30. They are wildly off by over 10 kg! You don't even need to calculate the exact decimal. You can instantly mark "None of these" within 5 seconds based on magnitude alone. ### Common Pitfall A common mistake is applying the correction backwards (adding it instead of subtracting it) or trying to find the total sum ($75 \times 47 = 3525$), doing the subtraction ($3525 - 20 = 3505$), and then doing long division ($3505 / 75$). This wastes immense time and introduces multiple points for arithmetic failure. Always correct the *average* directly using the difference. ### Final Answer **Therefore, the correct answer is None of these.**