Average score of 50 students in a class is 44. Later on it was found that the score 23 was incorrectly recorded as 73 . The correct average score is

Options

A. 21.5
B. 0.5
C. 43
D. None of these

Answer

To find the correct average score after correcting the misrecorded score, we can follow these steps:

### Step 1: Calculate the total score based on the initial average.
The average score of 50 students is given as 44. To find the total score, we use the formula:

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

Substituting the values:

\[ \text{Total Score} = 44 \times 50 = 2200 \]

### Step 2: Identify the incorrect score and the correct score.
It was found that the score of 23 was incorrectly recorded as 73. Therefore, we need to adjust the total score by removing the incorrect score and adding the correct score.

\[ \text{Incorrect Score} = 73 \]
\[ \text{Correct Score} = 23 \]

### Step 3: Adjust the total score.
To find the corrected total score, we subtract the incorrect score and add the correct score:

\[ \text{Corrected Total Score} = \text{Total Score} - \text{Incorrect Score} + \text{Correct Score} \]

Substituting the values:

\[ \text{Corrected Total Score} = 2200 - 73 + 23 = 2200 - 50 = 2150 \]

### Step 4: Calculate the new average score.
Now, we can find the new average score using the corrected total score:

\[ \text{New Average} = \frac{\text{Corrected Total Score}}{\text{Number of Students}} \]

Substituting the values:

\[ \text{New Average} = \frac{2150}{50} = 43 \]

### Final Answer
The correct average score is **43**.

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