The mode of the data `6,4,3,6,4,3,4,6,3,x` can be

Options

A. only 5
B. both 4 and 6
C. both 3 and 6
D. 3, 4 or 6

Answer

To determine the mode of the data set \(6, 4, 3, 6, 4, 3, 4, 6, 3, x\), we will follow these steps:

### Step 1: Count the occurrences of each number
First, we count how many times each number appears in the data set without \(x\):
- The number 6 appears 3 times.
- The number 4 appears 3 times.
- The number 3 appears 3 times.

### Step 2: Analyze the impact of \(x\)
Next, we need to consider the possible values of \(x\) and how they affect the mode:
- If \(x = 3\): The count of 3 becomes 4 (3 appears 4 times), while 4 and 6 still appear 3 times. Thus, the mode is 3.
- If \(x = 4\): The count of 4 becomes 4 (4 appears 4 times), while 3 and 6 still appear 3 times. Thus, the mode is 4.
- If \(x = 6\): The count of 6 becomes 4 (6 appears 4 times), while 3 and 4 still appear 3 times. Thus, the mode is 6.
- If \(x\) is any number other than 3, 4, or 6: The counts remain the same (3 appears 3 times, 4 appears 3 times, and 6 appears 3 times). Thus, there is no unique mode, and the mode remains 3, 4, or 6.

### Conclusion
The mode of the data set can be:
- 3 if \(x = 3\)
- 4 if \(x = 4\)
- 6 if \(x = 6\)
- 3, 4, or 6 if \(x\) is any other number.

### Final Answer
The mode of the data can be 3, 4, or 6 depending on the value of \(x\).

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