Final answer:
To maintain an ordered list, insert and remove methods need to be altered to ensure numbers are placed and maintained in sequence, which in turn allows searching methods like binary search and calculations such as finding the median to be more efficient.
Step-by-step explanation:
To keep the numbers in order from smallest to largest in a bag's list, you would need to alter methods that add or remove numbers to ensure they maintain order. For instance, if you're inserting a new number, you need to find the correct position in the sequence to insert it rather than just adding it to the end. If the numbers are already ordered, searching and retrieval methods like binary search could operate more efficiently, as they take advantage of the ordering to reduce the number of comparisons needed.
When considering removing numbers, it's also vital to shift all the larger numbers down in the list to fill the gap and maintain the ordering. Other operations such as calculating the median or finding the modes become more straightforward because the data doesn't need to be sorted every time you want to perform these calculations.