The average of 25 observations is 13. It was later found that an observation 73 was wrongly entered as 48. The new average is:

Options

A. 12.6
B. 14
C. 15
D. 13.8

Answer

To find the new average after correcting the wrongly entered observation, we can follow these steps:

### Step 1: Calculate the initial sum of observations
The average of 25 observations is given as 13. We can calculate the total sum of these observations using the formula:

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

Substituting the values:

\[ \text{Sum} = 13 \times 25 = 325 \]

### Step 2: Identify the incorrect and correct observations
An observation of 73 was wrongly entered as 48. We need to adjust the sum to reflect the correct observation.

### Step 3: Adjust the sum
To correct the sum, we need to remove the incorrect observation (48) and add the correct observation (73):

\[ \text{Corrected Sum} = \text{Initial Sum} - \text{Incorrect Observation} + \text{Correct Observation} \]

Substituting the values:

\[ \text{Corrected Sum} = 325 - 48 + 73 \]

Calculating this:

\[ \text{Corrected Sum} = 325 - 48 + 73 = 325 - 48 + 73 = 350 \]

### Step 4: Calculate the new average
Now that we have the corrected sum, we can find the new average using the same formula:

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

Substituting the values:

\[ \text{New Average} = \frac{350}{25} \]

Calculating this:

\[ \text{New Average} = 14 \]

### Final Answer
The new average is **14**.

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