Answer: C. $\text{13}$

Explanation:1. Understand the problem: The table shows the frequency of different values in a data set. We need to find the minimum value of this data set.

2. Interpret the frequency table (Source [291]): The table is structured as:

The "Value" column lists the actual numbers that are part of the data set. The "Frequency" column indicates how many times each of these distinct values occurs.

3. Identify the minimum value in the data set: To find the minimum value of the data set, we look at the numbers listed in the "Value" column and select the smallest one. The values listed are $\text{13}$, $\text{20}$, $\text{27}$, and $\text{34}$. The minimum among these values is $\text{13}$.

4. Compare with the given options: [A] $\text{1}$ (This value is not listed in the "Value" column of the data set.) [B] $\text{8}$ (This is a frequency, not a value from the data set's "Value" column.) [C] $\text{13}$ (This is the smallest value listed in the "Value" column.) [D] $\text{20}$ (This is one of the values in the data set, but it is not the minimum.)

5. Conclusion: The minimum value of the data set is $\text{13}$.