Okay, let's tackle this problem. The question is about calculating the correct mean weight after a mistake in recording one of the boys' weights. The initial mean was 18.2 kg for 10 boys, but one boy's weight was recorded as 2.0 kg instead of 20 kg. I need to find the true mean.

First, I remember that the mean is the total sum divided by the number of observations. So the original total sum would be 18.2 kg multiplied by 10 boys, which is 182 kg. But there's an error in one of the weights. The incorrect entry was 2.0 kg, which should have been 20 kg. That means the total sum was undercounted by 18 kg (20 - 2 = 18). So the correct total sum should be 182 + 18 = 200 kg. Then, dividing by 10 boys gives a new mean of 20 kg.

Wait, let me check again. Original total is 18.2 * 10 = 182. Subtract the incorrect 2 kg and add the correct 20 kg. So 182 - 2 + 20 = 200. Divided by 10, that's 20. So the correct mean is 20 kg.

Looking at the options, the correct answer should be 20 kg. The other options might be lower or higher. For example, if someone forgot to add the 18 kg, they might have 18.2 again. Or maybe they did the subtraction wrong. The key is to adjust the total sum correctly. The calculation seems straightforward once you remember to correct the total before recalculating the mean.

**Core Concept**
This question tests understanding of statistical correction in mean calculation. The mean is calculated as total sum divided by the number of observations. An error in one data point requires recalculating the total sum and then the new mean.

**Why the Correct Answer is Right**
Original mean = 18.2 kg for 10 boys → Total weight = 18.2 × 10 = 182 kg.
The incorrect weight (2.0 kg) was subtracted and replaced with the correct value (20 kg).
Corrected total weight = 182 - 2 + 20 = 200 kg.
New mean = 200 ÷ 10 = **20 kg**.
This adjustment accounts for the 18 kg difference (20 - 2) in the total sum.

**Why Each Wrong Option is Incorrect**
**Option A:** Likely reflects incorrect arithmetic (e.g., adding 2 instead of subtracting).
**Option B:** May stem from forgetting to adjust the total sum entirely.
**Option C:** Could result from miscalculating the difference (e.g., using 20 - 18.2 instead of 20 - 2).

**Clinical Pearl / High-Yield Fact**
Always verify total sums when correcting data errors. A single outlier can drastically alter the mean—recalculate the total sum first, then divide by the sample size. Use **"Total = Mean ×

✓ Correct Answer: D. 20 kg