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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This depends. There may be multiple studies, and someone might report that the success rate was between 30% and 80%.
Or, based on one or multiple studies, someone might say that the true success rate is between 30% and 80% (with 95% confidence).
That part in parentheses — “with 95% confidence” (or 98% or 99% or etc) — is sometimes unstated, but it’s not sleight of hand. There is an amazing result in statistics called the central limit theorem (CLT) that allows you to ‘bound’ the range of particular numbers.
There are some limitations to the CLT. It’s only approximately true, and only applies when you have a lot of data. (Also, it won’t work if your numbers have a very weird distribution, but that goes way beyond ELI5.) But it works for a huge number of statistics (including success rates).
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