Why is dictionary so much faster than list?

The reason is because a dictionary is a lookup, while a list is an iteration.

Dictionary uses a hash lookup, while your list requires walking through the list until it finds the result from beginning to the result each time.

to put it another way. The list will be faster than the dictionary on the first item, because there's nothing to look up. it's the first item, boom.. it's done. but the second time the list has to look through the first item, then the second item. The third time through it has to look through the first item, then the second item, then the third item.. etc..

So each iteration the lookup takes more and more time. The larger the list, the longer it takes. While the dictionary is always a more or less fixed lookup time (it also increases as the dictionary gets larger, but at a much slower pace, so by comparison it's almost fixed).

When you do this:

student.Grade = grades.Single(x => x.StudentId == student.Id).Value;

As written it has to enumerate the entire List until it finds the entry in the List that has the correct studentId (does entry 0 match the lambda? No... Does entry 1 match the lambda? No... etc etc). This is O(n). Since you do it once for every student, it is O(n^2).

However when you do this:

student.Grade = dic[student.Id];

If you want to find a certain element by key in a dictionary, it can instantly jump to where it is in the dictionary - this is O(1). O(n) for doing it for every student. (If you want to know how this is done - Dictionary runs a mathematical operation on the key, which turns it into a value that is a place inside the dictionary, which is the same place it put it when it was inserted)

So, dictionary is faster because you used a better algorithm.

When using Dictionary you are using a key to retrieve your information, which enables it to find it more efficiently, with List you are using Single Linq expression, which since it is a list, has no other option other than to look in entire list for wanted the item.

Dictionary uses hashing to search for the data. Each item in the dictionary is stored in buckets of items that contain the same hash. It's a lot quicker.

Try sorting your list, it will be a a bit quicker then.