Mean of 40 numbers is 37.5. If one of these numbers is taken as 53 instead of 35, find the correct mean.

Answer

To find the correct mean after correcting the value from 53 to 35, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Mean of 40 numbers = 37.5
- One of the numbers is incorrectly taken as 53 instead of 35.

2. **Calculate the Incorrect Sum of the Numbers**:
- The formula for mean is:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]
- Rearranging the formula to find the sum:
\[ \text{Sum} = \text{Mean} \times \text{Number of observations} \]
- Substitute the values:
\[ \text{Sum} = 37.5 \times 40 = 1500 \]
- So, the incorrect sum of the numbers is 1500.

3. **Adjust the Incorrect Sum**:
- To find the correct sum, we need to subtract the incorrect value (53) and add the correct value (35):
\[ \text{Correct Sum} = \text{Incorrect Sum} - \text{Incorrect Value} + \text{Correct Value} \]
- Substitute the values:
\[ \text{Correct Sum} = 1500 - 53 + 35 \]
- Calculate:
\[ \text{Correct Sum} = 1500 - 53 + 35 = 1482 \]

4. **Calculate the Correct Mean**:
- Now, we can find the correct mean using the correct sum:
\[ \text{Correct Mean} = \frac{\text{Correct Sum}}{\text{Number of observations}} \]
- Substitute the values:
\[ \text{Correct Mean} = \frac{1482}{40} \]
- Calculate:
\[ \text{Correct Mean} = 37.05 \]

### Final Answer:
The correct mean is **37.05**.