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

Answer

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

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

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

Rearranging this formula gives us:

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

Substituting the given values:

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

### Step 2: Identify the incorrect and correct values.
The incorrect value that was entered is 48, and the correct value should be 73.

### Step 3: Adjust the total sum to reflect the correct observation.
To find the new total sum, we need to replace the incorrect value with the correct value:

\[ \text{New Total Sum} = \text{Old Total Sum} - \text{Incorrect Value} + \text{Correct Value} \]

Substituting the values we have:

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

Calculating this gives:

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

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

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

Substituting the values:

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

Calculating this gives:

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

### Final Answer:
The new average after correcting the observation is **14**.

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