A raw data is in ascending order, i.e. 3,4,7,x,x + 1, 12, 13, 15 . If the median of this data is 9.5, then x is equal to :

Options

A. 7.5
B. 8.5
C. 8
D. 9

Answer

To solve the problem, we need to find the value of \( x \) in the given ascending data set: \( 3, 4, 7, x, x + 1, 12, 13, 15 \) such that the median of this data is \( 9.5 \).

### Step-by-Step Solution:

1. **Identify the number of data points**:
The data points are \( 3, 4, 7, x, x + 1, 12, 13, 15 \).
There are a total of 8 data points.

2. **Determine the position of the median**:
Since there are 8 data points (an even number), the median is calculated as the average of the 4th and 5th data points.
\[ \text{Median} = \frac{\text{4th observation} + \text{5th observation}}{2} \]

3. **Identify the 4th and 5th observations**:
In the ordered data, the 4th observation is \( x \) and the 5th observation is \( x + 1 \).

4. **Set up the equation for the median**:
According to the problem, the median is given as \( 9.5 \). Therefore, we can write:
\[ \frac{x + (x + 1)}{2} = 9.5 \]

5. **Simplify the equation**:
Combine the terms in the numerator:
\[ \frac{2x + 1}{2} = 9.5 \]

6. **Multiply both sides by 2 to eliminate the fraction**:
\[ 2x + 1 = 19 \]

7. **Solve for \( x \)**:
Subtract 1 from both sides:
\[ 2x = 18 \]
Now divide by 2:
\[ x = 9 \]

### Conclusion:
The value of \( x \) is \( 9 \).