I don’t even know if the question is well written but this is my doubt: sometimes (in the area of medicine in my case) you can read numbers like “between 30 and 80 percent of the patients have a relapse”.
Isn’t a percentage an average per se?
If I do an experiment with 100 people, shouldn’t I have an exact percentage of people who react in certain way? How can’t I know if they are 30 or 80?
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If you flip a coin twice and get heads both times, does that mean that coin will continue to give heads in the future 100% of the time?
That would be nuts.
You can do a study and count how many times something happened.
Then you have to predict how it will do in the future.
A huge and fundamental part of science is really just being able to make predictions.
It’s that bridge between “this is what *did* happen” and “this is what *will* happen” where the uncertainty comes from.
When you’re making predictions based on statistical evidence, there is always going to be some amount of uncertainty because, hey, maybe it was just a coincidence.
Note that the level of uncertainty goes down the more trials you do (the more times you flip your coin).
Flipping a coin twice and getting heads both times doesn’t really tell you much.
If you flip a coin 10 times and get heads 7 times, you still don’t have enough data to say with confidence that the coin is biased (it could just be a coincidence).
If you flip a coin 100 times and get heads 70 times, though, *now* you’ve got enough data to confidently say that the coin is biased towards heads (maybe the tails side is a bit heavier).
Specifically you can say with 95% confidence that the coin will continue to give heads between 61% and 79% of the time.
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