Qual è la differenza tra She is by far the best singer in her class. e She is much the best singer in her class. ?Sentiti libero di rispondere con un esempio.

hmm good question. maybe it's like this:

much: a large amount
by far: with a large difference

for example:
if we have an hour break. 50 minutes we spent outside. 5 minutes we spent in the kitchen. 5 minutes we spent in the office.

we can say

"much of our break time was spent outside"
or
"by far, most of our break time was spent outside."
or
"we spent much more time outside during break than inside"

so you can say "she is a much better singer than everyone else in her class"
or
"she is by far the best singer in her class"

they mean the same thing, but "by far" is more positive. When we compare using "much better than", it focuses a little more on the other people not being as good.

other common uses of "much":
(I ate) too much
(I didn't eat very) much
(I don't like it very) much
much of (something is something)

"by far" needs to be the most, least, greatest, worst, etc. compared to others. but it is (or feels like) *definitely* the most, least,greatest, worst etc.

"she is by far the nicest person I've ever met"
"she's so much nicer than anyone else I've ever met"
= I've met other people nice people, but oh my god she's SO NICE. #1 nice!

"she's much nicer than other people I've met"
=feels more like the other people here aren't very nice.

also, both of these are ok too:

"We had a competition, and Kim is by far the fastest student in our school!"
=we know Kim is much faster than the other students.

"Kim must be the fastest student in our school by far!"
=Kim is probably the fastest student in our school.

sorry it's long! I hope it helps.