The tests to show this include tens of thousands of words a highly educated English speaker would know. And they would use most of these only for specialised subjects or quizzes and general knowledge tests. Many would be very old words either rarely used or no longer used. Or not used in daily conversation. The normal average person would use 5,000 to 10,000 in their "normal" life. A person who did not attend any schooling would use about 3,000 in their everyday live. The average score for a native born English speaker using the various tests would be 30,000 to 35,000 words 25,000 are no use to them for daily conversation. Second language learners of English typically score up to 10,000 words using the various useless and fun only tests. 

A simple google search shows this:

"Studies have shown that the average English native speaker knows about 20,000 words with university-educated people knowing around 40,000 words."

I`m not too sure how you would even test this in any kind of study. I suppose you could take a book, a novel, something at about the college level, have someone read it and write down ever word her or she didn’t know. You could have the numbers of different words in the book counted first (imagine how tedious that would be) and then do some tally of how many of the words the person knew and put some number on it. It may have been tested like that before. It`s hard to say.

But, then there`s a whole body of speciality vocabulary only those in a specialized field knows, like law for example. Anyone know what a demurrer is in American law (maybe British law too)? I do. Not that it matters, but it`s not important for non-lawyers to know. Or a tort (not the kind you eat)? Medicine has its own nomenclature too. But the number of words an average person needs to know to understand a movie, for instance? 20,000-30,000 seems right to me, if you toss in colloquialisms and idioms too.