Data Analysis: Finding Equal Values in Student-Ball Number Table

To solve this problem, we can follow these logical steps:

• Step 1: Identify the pattern in the relationships between balls and students.
• Step 2: Test a basic arithmetic operation to see which consistently relates the number of balls to the number of students.
• Step 3: Verify calculation consistency across all pairs in the table.

Let's begin: From the table, we have the following mappings:

• For 2 balls, there are 100 students. Testing $\text{balls} \times 50 = 2 \times 50 = 100$.
• For 4 balls, there are 200 students. Testing $\text{balls} \times 50 = 4 \times 50 = 200$.
• For 6 balls, there are 300 students. Testing $\text{balls} \times 50 = 6 \times 50 = 300$.

In each case, multiplying the number of balls by 50 gives the number of students, confirming the relationship: The number of balls multiplied by 50 is equal to the number of students.

Thus, the correct operation to fill in the blank is "multiplied by 50."

Therefore, the number of balls multiplied by 50 is equal to the number of students.