While finding the average of 10 given numbers, a student, by mistake, wrote 64 in place of a number 46 and got his correct average 50. The correct average of the given numbers is :

Options

A. 48.2
B. 48.3
C. 49.1
D. 49.3

Answer

To find the correct average of the given numbers, we can follow these steps:

### Step 1: Understand the concept of average
The average of a set of numbers is calculated by dividing the sum of those numbers by the total count of the numbers.

### Step 2: Calculate the incorrect sum
The student calculated the average as 50 for 10 numbers. Therefore, the sum of the numbers he calculated is:
\[ \text{Sum} = \text{Average} \times \text{Count} = 50 \times 10 = 500 \]

### Step 3: Identify the incorrect number
The student mistakenly wrote 64 instead of the correct number 46. Therefore, the incorrect sum includes 64 instead of 46.

### Step 4: Calculate the difference caused by the mistake
To find the correct sum, we need to replace the incorrect number (64) with the correct number (46):
\[ \text{Correct Sum} = \text{Incorrect Sum} - \text{Incorrect Number} + \text{Correct Number} \]
\[ \text{Correct Sum} = 500 - 64 + 46 \]
\[ \text{Correct Sum} = 500 - 64 + 46 = 482 \]

### Step 5: Calculate the correct average
Now that we have the correct sum, we can find the correct average by dividing the correct sum by the count of numbers:
\[ \text{Correct Average} = \frac{\text{Correct Sum}}{\text{Count}} = \frac{482}{10} = 48.2 \]

### Final Answer
The correct average of the given numbers is **48.2**.

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