The mean of 25 values was 40 . But one value was written as 25 instead of 50 . The corrected means is .
A.39
B.41
C.40
D. 42

Options

A. D
B. B
C. C
D. A

Answer

To solve the problem, we need to find the corrected mean after identifying the error in one of the values.

### Step-by-Step Solution:

1. **Calculate the original sum of the values:**
The mean of the 25 values is given as 40. The formula for the mean is:
\[ \text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} \]
Rearranging this gives us:
\[ \text{Sum of values} = \text{Mean} \times \text{Number of values} = 40 \times 25 = 1000 \]

**Hint:** To find the sum from the mean, multiply the mean by the total number of values.

2. **Identify the error in the values:**
One value was incorrectly recorded as 25 instead of 50. This means that the original sum of 1000 includes the incorrect value of 25.

3. **Adjust the sum for the correction:**
To correct the sum, we need to remove the incorrect value (25) and add the correct value (50):
\[ \text{Corrected Sum} = \text{Original Sum} - \text{Incorrect Value} + \text{Correct Value} \]
Substituting the values:
\[ \text{Corrected Sum} = 1000 - 25 + 50 = 1000 + 25 = 1025 \]

**Hint:** When correcting a value, subtract the incorrect value and add the correct value to the original sum.

4. **Calculate the new mean:**
Now that we have the corrected sum, we can find the new mean:
\[ \text{New Mean} = \frac{\text{Corrected Sum}}{\text{Number of values}} = \frac{1025}{25} \]
Performing the division:
\[ \text{New Mean} = 41 \]

**Hint:** To find the mean after correction, divide the corrected sum by the total number of values.

### Final Answer:
The corrected mean is **41**.