The mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on it was found that three observations were incorrect, which are recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.

Explanation

To solve the problem step by step, we will follow the outlined procedure to find the corrected mean and standard deviation after omitting the incorrect observations.

### Step 1: Calculate the sum of the incorrect observations
The mean of the original 100 observations is given as 20. Therefore, the total sum of these observations can be calculated as follows:

\[ \text{Sum of observations} = \text{Mean} \times \text{Number of observations} = 20 \times 100 = 2000 \]
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