The median of the following numbers arranged in ascending order is 2.5, if so find x?
0,0,1,1, 2, 2, x, 3, 3, 4, 5, 7
A. 2
B. 3
C. 4
D. 0

Options

A. C
B. A
C. B
D. D

Answer

To find the value of \( x \) such that the median of the numbers \( 0, 0, 1, 1, 2, 2, x, 3, 3, 4, 5, 7 \) arranged in ascending order is \( 2.5 \), we can follow these steps:

### Step 1: Understand the median
The median of a set of numbers is the middle value when the numbers are arranged in order. If there is an even number of observations, the median is the average of the two middle values.

### Step 2: Count the total number of values
In the given set, we have 12 numbers (including \( x \)). Since 12 is an even number, the median will be the average of the 6th and 7th numbers in the ordered list.

### Step 3: Arrange the numbers
The numbers in ascending order are:
\[ 0, 0, 1, 1, 2, 2, x, 3, 3, 4, 5, 7 \]

### Step 4: Identify the positions for the median
The 6th and 7th numbers in this arrangement will determine the median. Currently, the 6th number is \( 2 \) and the 7th number is \( x \).

### Step 5: Set up the median equation
For the median to be \( 2.5 \):
\[ \text{Median} = \frac{\text{6th number} + \text{7th number}}{2} = 2.5 \]
Substituting the known values:
\[ \frac{2 + x}{2} = 2.5 \]

### Step 6: Solve for \( x \)
Multiply both sides by 2 to eliminate the fraction:
\[ 2 + x = 5 \]
Now, subtract 2 from both sides:
\[ x = 5 - 2 \]
\[ x = 3 \]

### Conclusion
The value of \( x \) that makes the median \( 2.5 \) is \( 3 \).

### Final Answer
**B. 3**