Mean  and standard deviation of 100 observations were found to be 40 and 10 respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively. Find the correct standard deviation.

Explanation

To find the correct standard deviation after correcting the wrongly recorded observations, we can follow these steps:

### Step 1: Calculate the incorrect summation of observations
Given:
- Mean (incorrect) = 40
- Number of observations (n) = 100

Using the formula for mean:
...