If the mode of scores 36, 48, 36, 60, 48, 72, 72, x 100 surnames we is 48, find the value of x.

Answer

To find the value of \( x \) such that the mode of the scores \( 36, 48, 36, 60, 48, 72, 72, x, 100 \) is \( 48 \), we can follow these steps:

### Step 1: Count the occurrences of each score
We need to count how many times each score appears in the list:

- **36** appears **2 times**.
- **48** appears **2 times**.
- **60** appears **1 time**.
- **72** appears **2 times**.
- **100** appears **1 time**.
- **x** appears **1 time** (we will consider the value of \( x \) later).

### Step 2: Determine the condition for the mode
The mode is the number that appears most frequently. For the mode to be \( 48 \), it must appear more times than any other number.

### Step 3: Set up the equation
Currently, \( 48 \) appears **2 times**. To make \( 48 \) the mode, it must appear more than any other number. The other numbers that appear **2 times** are \( 36 \) and \( 72 \).

To achieve this, we can set \( x = 48 \). This will increase the count of \( 48 \) to **3 times**.

### Step 4: Verify the counts
If we set \( x = 48 \):
- **36** appears **2 times**.
- **48** appears **3 times** (2 original + 1 for \( x \)).
- **60** appears **1 time**.
- **72** appears **2 times**.
- **100** appears **1 time**.

Now, the counts are:
- \( 36: 2 \)
- \( 48: 3 \) (most frequent)
- \( 60: 1 \)
- \( 72: 2 \)
- \( 100: 1 \)

### Step 5: Conclusion
Since \( 48 \) appears the most frequently (3 times), it confirms that the mode is indeed \( 48 \). Therefore, the value of \( x \) must be:

\[ \boxed{48} \]