The average weight of a group of 53 girls was calculated as 58 kgs. It was later discovered that the weight of one of the girls was read as 65 kgs., whereas her actual weight was 45 kgs. What is the actual average weight of the group of 53 girls ? (rounded off to two digits after decimal)

Options

A. A. 57.62 kgs
B. B. 57.37 kgs
C. C. 58.37 kgs
D. D. 58.62 kgs

Answer

To find the actual average weight of the group of 53 girls after correcting the weight of one girl, we can follow these steps:

### Step 1: Calculate the total weight based on the initial average.
The average weight of the 53 girls is given as 58 kgs. To find the total weight, we use the formula:

\[ \text{Total Weight} = \text{Average Weight} \times \text{Number of Girls} \]

Substituting the values:

\[ \text{Total Weight} = 58 \, \text{kgs} \times 53 = 3074 \, \text{kgs} \]

### Step 2: Identify the error in the weight of one girl.
It was discovered that one girl's weight was recorded as 65 kgs instead of her actual weight of 45 kgs. Therefore, there was an excess of:

\[ \text{Excess Weight} = 65 \, \text{kgs} - 45 \, \text{kgs} = 20 \, \text{kgs} \]

### Step 3: Adjust the total weight to reflect the actual weight.
To find the actual total weight of the group, we need to subtract the excess weight from the previously calculated total weight:

\[ \text{Actual Total Weight} = 3074 \, \text{kgs} - 20 \, \text{kgs} = 3054 \, \text{kgs} \]

### Step 4: Calculate the new average weight.
Now that we have the actual total weight, we can find the new average weight using the same formula for average:

\[ \text{New Average Weight} = \frac{\text{Actual Total Weight}}{\text{Number of Girls}} \]

Substituting the values:

\[ \text{New Average Weight} = \frac{3054 \, \text{kgs}}{53} \approx 57.62264151 \, \text{kgs} \]

### Step 5: Round off the average weight to two decimal places.
Finally, we round the average weight to two decimal places:

\[ \text{Rounded Average Weight} \approx 57.62 \, \text{kgs} \]

### Final Answer:
The actual average weight of the group of 53 girls is **57.62 kgs**.

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