Let's find the mode of the given frequency distribution step by step. A mode is the value(s) that appear most frequently in a data set. Here's the data presented:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Value} & \text{Frequency} \\
\hline
0 & 8 \\
1 & 12 \\
2 & 15 \\
3 & 20 \\
4 & 20 \\
5 & 14 \\
\hline
\end{array}
\][/tex]
### Step 1: Identify the Maximum Frequency
First, we need to identify the maximum frequency from the list of frequencies:
- Frequencies: 8, 12, 15, 20, 20, 14
The maximum frequency here is 20.
### Step 2: Identify the Value(s) Corresponding to the Maximum Frequency
Next, we need to find which value(s) correspond to this maximum frequency of 20. Checking the table, we see:
- Value 3 has a frequency of 20
- Value 4 has a frequency of 20
Since both values 3 and 4 have the same maximum frequency of 20, they are both considered modes in this distribution.
### Conclusion
Therefore, the modes of the frequency distribution are the values 3 and 4.
So, the correct answer is:
[tex]\[ \text{3 and 4} \][/tex]
