1. **State the problem:** We are given a frequency distribution table with values of $x$ and their corresponding frequencies $f$. We need to find the mode, which is the value of $x$ that appears most frequently. 2. **List the frequencies:** - $x=1$ has frequency $6$ - $x=2$ has frequency $20$ - $x=3$ has frequency $11$ - $x=4$ has frequency $17$ - $x=5$ has frequency $10$ 3. **Identify the highest frequency:** The highest frequency is $20$ which corresponds to $x=2$. 4. **Conclusion:** The mode is the value of $x$ with the highest frequency, so $$\text{Mode} = 2$$ This means $2$ is the most frequently occurring value in the data set.