The average weight of 25 bags is 55 kg. The weight of one bags was misred as 65 instead of 56. find the correct mean values
A. 55.25
B. 55.36
C. 54.64
D. 55.65

Options

A. A
B. C
C. B
D. D

Answer

To find the correct mean value of the weights of the bags after correcting the misread weight, we can follow these steps:

### Step 1: Calculate the total weight of the 25 bags
The average weight of the 25 bags is given as 55 kg. To find the total weight, we can use the formula:

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

Substituting the values:

\[ \text{Total Weight} = 55 \, \text{kg} \times 25 = 1375 \, \text{kg} \]

### Step 2: Identify the misread weight and the correct weight
The weight of one bag was misread as 65 kg instead of the correct weight of 56 kg.

### Step 3: Adjust the total weight
To find the correct total weight, we need to subtract the misread weight and add the correct weight:

\[ \text{Correct Total Weight} = \text{Total Weight} - \text{Misread Weight} + \text{Correct Weight} \]

Substituting the values:

\[ \text{Correct Total Weight} = 1375 \, \text{kg} - 65 \, \text{kg} + 56 \, \text{kg} \]

Calculating this:

\[ \text{Correct Total Weight} = 1375 - 65 + 56 = 1366 \, \text{kg} \]

### Step 4: Calculate the new mean value
Now, we can find the new mean by dividing the correct total weight by the number of bags:

\[ \text{New Mean} = \frac{\text{Correct Total Weight}}{\text{Number of Bags}} = \frac{1366 \, \text{kg}}{25} \]

Calculating this:

\[ \text{New Mean} = 54.64 \, \text{kg} \]

### Conclusion
The correct mean value of the weights of the bags after adjustment is **54.64 kg**.