If the number 13, 15, 17, 18 and n are arranged in ascending order and their arithmetic mean and median are equal then va lue of n will be

Answer

To solve the problem, we need to find the value of \( n \) such that the arithmetic mean and median of the numbers \( 13, 15, 17, 18, \) and \( n \) are equal when arranged in ascending order.

### Step-by-Step Solution:

1. **Identify the Numbers**: The numbers we have are \( 13, 15, 17, 18, \) and \( n \).

2. **Determine the Median**:
- Since there are 5 numbers, the median will be the 3rd number when arranged in ascending order.
- The median is given as \( 17 \) (since it is the middle number when sorted).

3. **Set Up the Condition for the Mean**:
- The arithmetic mean is calculated as:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]
- The sum of the observations is \( 13 + 15 + 17 + 18 + n = 63 + n \).
- The number of observations is \( 5 \).
- Therefore, the mean can be expressed as:
\[ \text{Mean} = \frac{63 + n}{5} \]

4. **Set the Mean Equal to the Median**:
- Since we know that the mean and median are equal, we can set up the equation:
\[ \frac{63 + n}{5} = 17 \]

5. **Solve for \( n \)**:
- Multiply both sides by \( 5 \):
\[ 63 + n = 85 \]
- Subtract \( 63 \) from both sides:
\[ n = 85 - 63 \]
- Therefore:
\[ n = 22 \]

6. **Conclusion**: The value of \( n \) is \( 22 \).