The average of 50 results was calculated as 30 but later it was found that while calculating, 73 was taken as 33 by mistake, then what will be the correct average?

Options

A. 29.2
B. 30.8
C. 31.6
D. 34

Answer

To find the correct average after identifying the mistake in the calculation, we can follow these steps:

### Step 1: Calculate the total of the original average
The average of 50 results is given as 30. To find the total sum of these results, we can use the formula for average:

\[ \text{Average} = \frac{\text{Total Sum}}{\text{Number of Observations}} \]

Rearranging this gives us:

\[ \text{Total Sum} = \text{Average} \times \text{Number of Observations} \]

Substituting the values:

\[ \text{Total Sum} = 30 \times 50 = 1500 \]

### Step 2: Identify the mistake in the calculation
It was found that 73 was mistakenly taken as 33. Therefore, we need to calculate the difference caused by this mistake:

\[ \text{Difference} = 73 - 33 = 40 \]

### Step 3: Adjust the total sum for the correct value
Since we initially subtracted 33 instead of adding 73, we need to add the difference back to the total sum:

\[ \text{Correct Total Sum} = \text{Original Total Sum} + \text{Difference} \]

Substituting the values:

\[ \text{Correct Total Sum} = 1500 + 40 = 1540 \]

### Step 4: Calculate the new average
Now that we have the correct total sum, we can calculate the new average using the same formula:

\[ \text{New Average} = \frac{\text{Correct Total Sum}}{\text{Number of Observations}} \]

Substituting the values:

\[ \text{New Average} = \frac{1540}{50} = 30.8 \]

### Final Answer
The correct average is **30.8**.

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