Question: Find the median.
Table at center: two-column frequency table with headers $x$ and $f$.
Rows:
$x=2$, $f=1$
$x=4$, $f=4$
$x=6$, $f=8$
$x=8$, $f=5$
$x=10$, $f=2$
1. **State the problem:** Find the median of the data given in the frequency table with values $x$ and their frequencies $f$.
2. **List the data:**
\begin{align*}
x &: 2, 4, 6, 8, 10 \\
f &: 1, 4, 8, 5, 2
\end{align*}
3. **Calculate the total number of observations $N$:**
$$N = 1 + 4 + 8 + 5 + 2 = 20$$
4. **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.
5. **Construct cumulative frequency (CF) table:**
\begin{align*}
x &: 2, 4, 6, 8, 10 \\
f &: 1, 4, 8, 5, 2 \\
CF &: 1, 5, 13, 18, 20
\end{align*}
6. **Locate the median class:**
The 10th and 11th observations lie in the class where CF just exceeds or equals 10.
CF at $x=4$ is 5 (less than 10), CF at $x=6$ is 13 (greater than 10), so median class is $x=6$.
7. **Find the median value:**
Since the 10th and 11th values both fall in the $x=6$ group, the median is $6$.
**Final answer:**
$$\boxed{6}$$