Answered

Find the mode of the frequency distribution.

\begin{tabular}{l|l}
Value & Frequency \\
\hline
0 & 8 \\
1 & 12 \\
2 & 15 \\
3 & 20 \\
4 & 20 \\
5 & 14 \\
\end{tabular}

A. 20
B. 3
C. 4
D. 3 and 4
E. 3.5



Answer :

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]