If the mode of the scores 10, 12, 13, 15, 15, 13, 12, 10, x is 15, then what is the value of x?

Options

A. 10
B. 12
C. 13
D. 15

Answer

To find the value of \( x \) such that the mode of the scores \( 10, 12, 13, 15, 15, 13, 12, 10, x \) is 15, we can follow these steps:

### Step 1: Understand the concept of mode
The mode of a set of numbers is the number that appears most frequently. In this case, we need the mode to be 15.

### Step 2: Count the occurrences of each number
Let's count how many times each number appears in the given set (excluding \( x \)):
- 10 appears 2 times
- 12 appears 2 times
- 13 appears 2 times
- 15 appears 2 times

### Step 3: Determine how to make 15 the mode
Currently, 15 appears 2 times, which is the same frequency as 10, 12, and 13. To make 15 the mode, it needs to appear more frequently than any other number.

### Step 4: Set \( x \) to 15
If we set \( x = 15 \), then the frequency of 15 will increase to 3 times:
- 10: 2 times
- 12: 2 times
- 13: 2 times
- 15: 3 times (after including \( x \))

### Step 5: Conclusion
Since 15 will now appear 3 times, it will be the most frequent number in the set, making it the mode. Therefore, the value of \( x \) must be 15.

### Final Answer:
\( x = 15 \)

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