Question: Find the median.
x f
2 4
4 8
6 2
8 1
10 5
1. **State the problem:** Find the median of the data given in the frequency table with values $x = 2, 4, 6, 8, 10$ and frequencies $f = 4, 8, 2, 1, 5$.
2. **Calculate the total number of observations:**
$$n = 4 + 8 + 2 + 1 + 5 = 20$$
3. **Find the median position:**
Since $n=20$ is even, the median is the average of the $\frac{n}{2}$-th and $\left(\frac{n}{2} + 1\right)$-th observations.
$$\frac{n}{2} = 10$$
So, median is the average of the 10th and 11th values in the ordered data.
4. **Create the cumulative frequency table:**
| x | f | Cumulative Frequency |
|---|---|----------------------|
| 2 | 4 | 4 |
| 4 | 8 | 12 |
| 6 | 2 | 14 |
| 8 | 1 | 15 |
| 10| 5 | 20 |
5. **Locate the median class:**
The 10th and 11th observations fall in the cumulative frequency 12, which corresponds to $x=4$.
6. **Conclusion:**
The median is $4$ because both the 10th and 11th values correspond to $x=4$.
**Final answer:**
$$\boxed{4}$$