The ages of some students are given as $12$, $13$, $16$, $18$, $14$, $19$, $13$, $17$, $15$, and $11$ years. What is the **median age** of these students?

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**Solution:**

1. First, arrange the ages in ascending order:
   
   $$11, 12, 13, 13, 14, 15, 16, 17, 18, 19$$

2. Count the total number of students, which is $n = 10$ (an even number).

3. For an even number of observations, the median is the average of the values at positions $\frac{n}{2}$ and $\left(\frac{n}{2} + 1ight)$.

$$	ext{Median} = \frac{	ext{value at } 5^{th} + 	ext{value at } 6^{th}}{2}$$

4. Identify the $5^{th}$ and $6^{th}$ values in the ordered list:
   - $5^{th}$ value = $14$
   - $6^{th}$ value = $15$

5. Calculate the median:

$$	ext{Median} = \frac{14 + 15}{2} = \frac{29}{2} = 14.5$$

**Answer:** $14.5$

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