## **Core Concept**
The problem involves calculating the mean weight of a group of boys before and after correcting an incorrectly recorded weight. The mean weight is calculated by summing all the weights and dividing by the number of boys.

## **Why the Correct Answer is Right**
Initially, the mean weight of 10 boys was given as 18.2 kg. This means the total weight of the 10 boys, as initially recorded, was $18.2 times 10 = 182$ kg. However, one boy's weight was wrongly recorded as 2.0 kg instead of the correct weight of 20 kg. To find the true mean weight, we need to adjust the total weight by subtracting the incorrect weight (2.0 kg) and adding the correct weight (20 kg). The adjustment to the total weight is $20 - 2 = 18$ kg. Therefore, the corrected total weight is $182 + 18 = 200$ kg. The true mean weight of the group is then $frac{200}{10} = 20$ kg.

## **Why Each Wrong Option is Incorrect**
- **Option A:** This option suggests a calculation error leading to a mean that does not match any logical step in recalculating the mean based on the given data.
- **Option B:** This option implies $frac{182 - 2 + 20}{10} = frac{200}{10} = 20$, which actually matches our correct calculation but let's ensure other options are indeed incorrect.
- **Option C:** This would imply a different adjustment or calculation not supported by the details given in the problem.
- **Option D:** Similarly, this suggests an incorrect calculation not aligned with the provided numbers and the correction needed.

## **Clinical Pearl / High-Yield Fact**
In clinical and research settings, accurately recording and managing data is crucial. This question highlights the importance of accurate data entry and how errors can affect calculated values such as means, which are commonly used in medical research and practice to describe patient populations.

## **Correct Answer:** .