The average marks in Mathematics for 5 students was found to be 50 . Later it was discovered that in case of one student , the marks 48 were misread as 84 .The correct average is

Options

A. 40 . 2
B. 40 . 8
C. 42 . 8
D. 48 . 2

Answer

To find the correct average marks after correcting the misread marks, we can follow these steps:

### Step 1: Calculate the total marks based on the initial average.
The average marks for 5 students is given as 50. To find the total marks, we use the formula for average:

\[ \text{Average} = \frac{\text{Total Marks}}{\text{Number of Students}} \]

So, we can rearrange this to find the total marks:

\[ \text{Total Marks} = \text{Average} \times \text{Number of Students} = 50 \times 5 = 250 \]

### Step 2: Identify the misread marks and correct them.
It was discovered that one student's marks (originally read as 84) were actually 48. We need to adjust the total marks by removing the incorrect marks and adding the correct marks:

\[ \text{Corrected Total Marks} = \text{Total Marks} - \text{Misread Marks} + \text{Actual Marks} \]

Substituting the values:

\[ \text{Corrected Total Marks} = 250 - 84 + 48 \]

### Step 3: Calculate the corrected total marks.
Now we perform the calculation:

\[ \text{Corrected Total Marks} = 250 - 84 + 48 = 250 - 36 = 214 \]

### Step 4: Calculate the new average.
Now that we have the corrected total marks, we can find the new average:

\[ \text{New Average} = \frac{\text{Corrected Total Marks}}{\text{Number of Students}} = \frac{214}{5} \]

### Step 5: Perform the final calculation for the new average.
Calculating the new average:

\[ \text{New Average} = 42.8 \]

Thus, the correct average marks after the correction is **42.8**.

---