When we look at different ways to sort data, we see that there are two main types: recursive and iterative. These types can change how well the sorting works.

Merge Sort is a recursive method, and it usually works much better in real life than Bubble Sort, which is an iterative method that isn't as efficient.

1. How Fast They Work

• Merge Sort is really fast with a performance level of $O(n \log n)$. This means it’s great for handling lots of data. It works by splitting data in half, sorting each half, and then putting them back together.
• Bubble Sort is slower, with a performance level of $O(n^2)$. It compares two things at a time and switches them around, which makes it drag its feet, especially with bigger datasets.

2. Example: Sorting Student Grades

Imagine a university needs to sort a long list of student grades. If there are thousands of students:

• Using Merge Sort would make this task much quicker because it merges the sorted lists easily.
• Using Bubble Sort would take a lot of time, especially if the grades are almost sorted already, because it has to go through the list many times.

3. Keeping Things in Order

Merge Sort is good at keeping equal items in the same order. This is important if some students have the same grades. Bubble Sort also keeps order, but it does this less efficiently.

Conclusion

In the end, both Merge Sort and Bubble Sort can sort data. However, Merge Sort is much better because it’s faster, works well with large amounts of data, and keeps order. This makes it the better choice for practical use in computer science.