The average age of 40 students in a class is 75 kg. By mistake the weights of two students were read as 74 kg and 66 kg respectively instead of 66 kg and 54 kg respectively. Find the corrected average of the class?

The problem involves correcting the average weight of a class of students due to an error in recording the weights of two students.

### Given:
- The average weight of 40 students is **75 kg**.
- The total weight of 40 students is:
\[
\text{Total weight} = 40 \times 75 = 3000 \, \text{kg}.
\]

### The weights that were recorded incorrectly:
- Instead of **66 kg**, **74 kg** was recorded.
- Instead of **54 kg**, **66 kg** was recorded.

### Steps to find the corrected total weight:
1. **Sum of the incorrect weights**:
   \[
   74 \, \text{kg} + 66 \, \text{kg} = 140 \, \text{kg}.
   \]
2. **Sum of the correct weights**:
   \[
   66 \, \text{kg} + 54 \, \text{kg} = 120 \, \text{kg}.
   \]
3. **Difference in weight**:
   \[
   140 \, \text{kg} - 120 \, \text{kg} = 20 \, \text{kg}.
   \]
   So, the recorded total weight is **20 kg more** than the actual total weight.

4. **Corrected total weight**:
   \[
   3000 \, \text{kg} - 20 \, \text{kg} = 2980 \, \text{kg}.
   \]

### Corrected average weight:
\[
\text{Corrected average} = \frac{2980}{40} = 74.5 \, \text{kg}.
\]

### Final Answer:
The corrected average weight of the class is **74.5 kg**.

---

Do you want further details or have any questions?

Here are some related questions for further practice:
1. How does a mistake in a few data points affect the overall average?
2. If one more student's weight was recorded incorrectly, how would you calculate the corrected average?
3. What is the impact on the average if the incorrect weights were overestimated?
4. How can you calculate the new total if the class size increases?
5. What is the relation between average and sum of a group of numbers?

**Tip:** Always verify your data when calculating averages to avoid misinterpretations!

Learn how to find the corrected average weight of a class of 40 students after correcting an error in the weights of two students. This problem involves key concepts such as averages and data correction, with a detailed step-by-step solution. Suitable for students in Grades 6-8.

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