2, 3, 5, 8, 2, 0, 8, 5, 4, 3, p, 2, 8
If the mode of given data is 8, then find the value of p:

Options

A. 3
B. 8
C. 2
D. 5

Answer

To solve the problem, we need to determine the value of \( p \) such that the mode of the given data set is 8. The mode is defined as the number that appears most frequently in a data set.

### Step-by-Step Solution:

1. **List the Given Data**:
The data provided is:
\[ 2, 3, 5, 8, 2, 0, 8, 5, 4, 3, p, 2, 8 \]

2. **Count the Frequency of Each Number**:
- Count how many times each number appears in the data set:
- **2** appears 3 times.
- **3** appears 2 times.
- **5** appears 2 times.
- **8** appears 3 times.
- **0** appears 1 time.
- **4** appears 1 time.
- **p** appears 1 time (until we determine its value).

3. **Determine the Current Mode**:
Currently, both 2 and 8 appear 3 times. Therefore, the mode is not uniquely defined yet, as both have the same frequency.

4. **Finding the Value of \( p \)**:
- For the mode to be 8, it must appear more frequently than any other number.
- If we set \( p = 8 \), then the frequency of 8 will increase to 4 (since it will appear 4 times).
- The frequency of 2 will remain at 3.
- Thus, 8 will be the mode because it appears more frequently than 2.

5. **Conclusion**:
Therefore, the value of \( p \) must be:
\[ p = 8 \]

### Final Answer:
\[ \text{The value of } p \text{ is } 8. \]