The average of 10 numbers is calculated as 15 it is discovered later on that while calculating the average one number namely 36 was wrongly read as 26 the correct average is

Options

A. A)12.4
B. B)14
C. C)16
D. D)18.6

Answer

To find the correct average after discovering the error in the calculation, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Incorrect Sum**:
The average of 10 numbers is given as 15. To find the sum of these numbers, we use the formula:
\[ \text{Sum} = \text{Average} \times \text{Number of Observations} \]
So,
\[ \text{Sum} = 15 \times 10 = 150 \]

**Hint**: Remember that the sum can be found by multiplying the average by the total number of items.

2. **Identify the Error**:
It is stated that one number, 36, was incorrectly read as 26. We need to adjust the sum to account for this error. The adjustment can be calculated as:
\[ \text{Adjustment} = \text{Correct Number} - \text{Wrong Number} = 36 - 26 = 10 \]

**Hint**: When correcting an error, subtract the incorrect value and add the correct value.

3. **Calculate the Correct Sum**:
To find the correct sum, we add the adjustment to the incorrect sum:
\[ \text{Correct Sum} = \text{Incorrect Sum} + \text{Adjustment} = 150 + 10 = 160 \]

**Hint**: Always ensure to add or subtract the difference to get the correct total.

4. **Calculate the Correct Average**:
Now, we can find the correct average by dividing the correct sum by the number of observations:
\[ \text{Correct Average} = \frac{\text{Correct Sum}}{\text{Number of Observations}} = \frac{160}{10} = 16 \]

**Hint**: The average is found by dividing the total sum by the number of items.

### Final Answer:
The correct average is **16**.