The average weight of a group of 20 boys was calculated to be 89.4 kg and it was later discovered that one weight was misread as 78 kg instead of the correct one of 87 kg. The correct average weight is

Answer

To find the correct average weight of the group of 20 boys after correcting the misread weight, we can follow these steps:

### Step 1: Calculate the total weight based on the incorrect average.
The average weight of the group was calculated to be 89.4 kg. Since there are 20 boys in the group, we can calculate the total weight using the formula:

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

Substituting the values:

\[ \text{Total Weight} = 89.4 \, \text{kg} \times 20 = 1788 \, \text{kg} \]

### Step 2: Identify the misread weight and the correct weight.
The weight was misread as 78 kg instead of the correct weight of 87 kg. We need to find the difference between the correct weight and the misread weight:

\[ \text{Difference} = \text{Correct Weight} - \text{Misread Weight} = 87 \, \text{kg} - 78 \, \text{kg} = 9 \, \text{kg} \]

### Step 3: Adjust the total weight to correct the misreading.
Since the weight was misread as 9 kg less than it should have been, we need to add this difference to the total weight calculated in Step 1:

\[ \text{Correct Total Weight} = \text{Total Weight} + \text{Difference} = 1788 \, \text{kg} + 9 \, \text{kg} = 1797 \, \text{kg} \]

### Step 4: Calculate the correct average weight.
Now that we have the correct total weight, we can find the correct average by dividing the corrected total weight by the number of boys:

\[ \text{Correct Average} = \frac{\text{Correct Total Weight}}{\text{Number of Boys}} = \frac{1797 \, \text{kg}}{20} = 89.85 \, \text{kg} \]

### Final Answer:
The correct average weight of the group of 20 boys is **89.85 kg**.

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