The mean of 100 items was found to be 30. If at the time of calculation two items were wrongly taken as 32 and 12 instead of 23 and 11, find the correct mean.

Explanation

To find the correct mean after correcting the wrongly taken values, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the total sum of the items based on the wrong mean:**
- The mean is given as 30 for 100 items.
- Therefore, the total sum (S) can be calculated using the formula:
\[
...