The mean of 30 values was 150. It was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean. Find the correct mean.

Options

A. 151
B. 149
C. 152
D. None of these

Answer

To find the correct mean after detecting the error in the recorded value, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Total Sum of the Original Values:**
The mean of the 30 values is given as 150. To find the total sum of these values, we can use the formula:
\[ \text{Total Sum} = \text{Mean} \times \text{Number of Values} \]
Substituting the given values:
\[ \text{Total Sum} = 150 \times 30 = 4500 \]

2. **Identify the Incorrect and Correct Values:**
The value that was incorrectly recorded is 135, and the correct value should be 165.

3. **Calculate the Difference Between the Correct and Incorrect Values:**
We need to find the difference between the correct value and the incorrect value:
\[ \text{Difference} = \text{Correct Value} - \text{Incorrect Value} = 165 - 135 = 30 \]

4. **Adjust the Total Sum:**
To find the correct total sum, we need to add the difference calculated in the previous step to the original total sum:
\[ \text{Correct Total Sum} = \text{Original Total Sum} + \text{Difference} = 4500 + 30 = 4530 \]

5. **Calculate the Correct Mean:**
Now, we can find the correct mean using the corrected total sum:
\[ \text{Correct Mean} = \frac{\text{Correct Total Sum}}{\text{Number of Values}} = \frac{4530}{30} \]
Performing the division:
\[ \text{Correct Mean} = 151 \]

### Final Answer:
The correct mean is **151**.

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