Step 1: Count the total number of observations

Count the given observations: $4, 14, 11, 8, 7, 8, 9, 12, 4, 6$. There are $n = 10$ terms (even number).

$n = 10$

Step 2: Arrange the observations in ascending order

Sorting the numbers from smallest to largest gives: $4, 4, 6, 7, 8, 8, 9, 11, 12, 14$.

$4, 4, 6, 7, 8, 8, 9, 11, 12, 14$

Step 3: Identify the middle terms

Since $n = 10$ is even, the median is the average of the $5^{\text{th}}$ and $6^{\text{th}}$ terms in the sorted list.

$5^{\text{th}} = 8, \quad 6^{\text{th}} = 8$

Step 4: Calculate the median

Compute the average of the two middle terms: $\frac{8 + 8}{2} = 8$.

$\text{Median} = \frac{8 + 8}{2} = 8$