Median of the following numbers
`4,4,5,7,6,7,7,12,3` is

Options

A. 4
B. 5
C. 6
D. 7

Explanation

To find the median of the given numbers \(4, 4, 5, 7, 6, 7, 7, 12, 3\), we will follow these steps:

### Step 1: Arrange the numbers in ascending order
First, we need to sort the numbers from the smallest to the largest.

The given numbers are:
\[ 4, 4, 5, 7, 6, 7, 7, 12, 3 \]

Arranging them in ascending order, we get:
\[ 3, 4, 4, 5, 6, 7, 7, 7, 12 \]

### Step 2: Count the number of observations
Next, we count how many numbers we have in the sorted list.

The sorted list is:
\[ 3, 4, 4, 5, 6, 7, 7, 7, 12 \]

Counting these, we find that there are \(9\) observations.

### Step 3: Determine if the number of observations is odd or even
Since \(9\) is an odd number, we will use the formula for finding the median in a dataset with an odd number of observations.

### Step 4: Find the median position
The formula to find the median position when the number of observations \(n\) is odd is:
\[ \text{Median position} = \frac{n + 1}{2} \]
Substituting \(n = 9\):
\[ \text{Median position} = \frac{9 + 1}{2} = \frac{10}{2} = 5 \]

### Step 5: Identify the median value
Now, we need to find the value at the \(5^{th}\) position in the sorted list:
\[ 3, 4, 4, 5, 6, 7, 7, 7, 12 \]

Counting to the \(5^{th}\) position, we see that it is \(6\).

### Conclusion
Thus, the median of the given numbers is:
\[ \text{Median} = 6 \]