The average weight of a class of 45 girls is 53 kg. It was later found that weight of two girls was read as 49 kg and 57 kg instead of 45 kg and 52 kg. Find the actual average weight of the class.

Options

A. A)54 kg
B. B)53.40 kg
C. C)50.6 kg
D. D)52.80 kg

Answer

To find the actual average weight of the class after correcting the weights of two girls, we can follow these steps:

### Step 1: Calculate the total weight based on the incorrect average.
The average weight of the class is given as 53 kg for 45 girls.

\[ \text{Total weight (incorrect)} = \text{Average} \times \text{Number of girls} = 53 \, \text{kg} \times 45 = 2385 \, \text{kg} \]

### Step 2: Determine the incorrect weights and the correct weights.
The weights that were incorrectly recorded are 49 kg and 57 kg. The correct weights should have been 45 kg and 52 kg.

### Step 3: Calculate the difference in total weight due to the incorrect readings.
The incorrect total weight added is:

\[ \text{Incorrect total weight} = 49 + 57 = 106 \, \text{kg} \]

The correct total weight should be:

\[ \text{Correct total weight} = 45 + 52 = 97 \, \text{kg} \]

### Step 4: Find the difference in weight.
Now, we find the difference between the incorrect total weight and the correct total weight:

\[ \text{Difference} = 106 \, \text{kg} - 97 \, \text{kg} = 9 \, \text{kg} \]

### Step 5: Adjust the total weight to find the correct total weight.
Now, we need to subtract this difference from the incorrect total weight:

\[ \text{Total weight (correct)} = \text{Total weight (incorrect)} - \text{Difference} = 2385 \, \text{kg} - 9 \, \text{kg} = 2376 \, \text{kg} \]

### Step 6: Calculate the correct average weight.
Now, we can find the correct average weight by dividing the correct total weight by the number of girls:

\[ \text{Average weight (correct)} = \frac{\text{Total weight (correct)}}{\text{Number of girls}} = \frac{2376 \, \text{kg}}{45} = 52.80 \, \text{kg} \]

### Final Answer
The actual average weight of the class is **52.80 kg**.

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