Average marks of maths of 5 students is 50. Later it was found that 48 was mistakenly reworded as 84. Find the actual average

Answer

To find the actual average marks of the 5 students after correcting the mistake, we can follow these steps:

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

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

Substituting the values:

\[ \text{Total Marks} = 50 \times 5 = 250 \]

### Step 2: Identify the mistake in the total marks.
It was found that 48 was mistakenly recorded as 84. To find the difference caused by this mistake, we calculate:

\[ \text{Difference} = \text{Mistaken Value} - \text{Actual Value} = 84 - 48 = 36 \]

### Step 3: Adjust the total marks to reflect the correct value.
Since the mistaken value was higher than the actual value, we need to subtract this difference from the total marks:

\[ \text{Correct Total Marks} = \text{Total Marks} - \text{Difference} = 250 - 36 = 214 \]

### Step 4: Calculate the actual average.
Now, we can find the actual average by dividing the corrected total marks by the number of students:

\[ \text{Actual Average} = \frac{\text{Correct Total Marks}}{\text{Number of Students}} = \frac{214}{5} = 42.8 \]

### Final Answer:
The actual average marks of the 5 students is **42.8**.

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