Find the median of the following data if the value of x = 4 ,
`x -4, 2x - 6, 3x-10 ,(x)/(2) - 1 , ( 3x)/( 2 x - 4) , x + 3, (x)/( 2), 2x + 7, 3x - 2, 2x -5`

Answer

To find the median of the given data when \( x = 4 \), we will follow these steps:

### Step 1: Substitute the value of \( x \)
We have the expressions:
1. \( x - 4 \)
2. \( 2x - 6 \)
3. \( 3x - 10 \)
4. \( \frac{x}{2} - 1 \)
5. \( \frac{3x}{2x - 4} \)
6. \( x + 3 \)
7. \( \frac{x}{2} \)
8. \( 2x + 7 \)
9. \( 3x - 2 \)
10. \( 2x - 5 \)

Substituting \( x = 4 \):

1. \( 4 - 4 = 0 \)
2. \( 2(4) - 6 = 8 - 6 = 2 \)
3. \( 3(4) - 10 = 12 - 10 = 2 \)
4. \( \frac{4}{2} - 1 = 2 - 1 = 1 \)
5. \( \frac{3(4)}{2(4) - 4} = \frac{12}{8 - 4} = \frac{12}{4} = 3 \)
6. \( 4 + 3 = 7 \)
7. \( \frac{4}{2} = 2 \)
8. \( 2(4) + 7 = 8 + 7 = 15 \)
9. \( 3(4) - 2 = 12 - 2 = 10 \)
10. \( 2(4) - 5 = 8 - 5 = 3 \)

### Step 2: Write the data set
From the above calculations, we have the following data set:
\[ 0, 2, 2, 1, 3, 7, 2, 15, 10, 3 \]

### Step 3: Arrange the data in ascending order
Arranging the data in ascending order:
\[ 0, 1, 2, 2, 2, 3, 3, 7, 10, 15 \]

### Step 4: Find the number of data points
Count the number of data points:
There are \( n = 10 \) data points.

### Step 5: Calculate the median
Since \( n \) is even, the median is given by the average of the \( \frac{n}{2} \)th term and the \( \left(\frac{n}{2} + 1\right) \)th term.

Calculating:
- \( \frac{n}{2} = 5 \)
- \( \frac{n}{2} + 1 = 6 \)

The 5th term is \( 2 \) and the 6th term is \( 3 \).

Now, calculate the median:
\[ \text{Median} = \frac{\text{5th term} + \text{6th term}}{2} = \frac{2 + 3}{2} = \frac{5}{2} = 2.5 \]

### Final Answer
The median of the data is \( 2.5 \).

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