The following observations have been arranged in the ascending order . If the median of the data `2, 3 ,x , x + 2, 11, 17 ` is 9 then the value of 3 x + 1 is ______

Options

A. 20
B. 8
C. 25
D. 12

Answer

To solve the problem step by step, we will follow the given observations and the information about the median.

### Step 1: Understand the Data
The given observations are:
\[ 2, 3, x, x + 2, 11, 17 \]

### Step 2: Determine the Number of Observations
We have a total of 6 observations (n = 6), which is even.

### Step 3: Median Formula for Even n
For an even number of observations, the median is calculated as:
\[ \text{Median} = \frac{\text{(n/2)th term} + \text{(n/2 + 1)th term}}{2} \]
Here, \( n/2 = 3 \) and \( n/2 + 1 = 4 \). Therefore, the median will be:
\[ \text{Median} = \frac{\text{3rd term} + \text{4th term}}{2} \]

### Step 4: Identify the 3rd and 4th Terms
From the arranged data:
- The 3rd term is \( x \)
- The 4th term is \( x + 2 \)

### Step 5: Set Up the Equation for the Median
According to the problem, the median is given as 9. Thus, we can set up the equation:
\[ \frac{x + (x + 2)}{2} = 9 \]

### Step 6: Simplify the Equation
Simplifying the equation:
\[ \frac{2x + 2}{2} = 9 \]
This simplifies to:
\[ x + 1 = 9 \]

### Step 7: Solve for x
Subtracting 1 from both sides gives:
\[ x = 9 - 1 = 8 \]

### Step 8: Calculate \( 3x + 1 \)
Now that we have the value of \( x \), we can find \( 3x + 1 \):
\[ 3x + 1 = 3(8) + 1 = 24 + 1 = 25 \]

### Final Answer
The value of \( 3x + 1 \) is:
\[ \boxed{25} \]