In 16 Books Dickens Used 37,504 Words

but just what that means is subject to various qualifications. For example:

I downcased everything, split hyphenated words, and counted only all-alphabetic tokens. Of course the 37,504 types constitute a smaller number of "word families" — thus we have

504 dog 200 dogs 32 dogged 27 doggedly 5 dogging 3 doglike 2 doggedness

The meaning and usage of dogged and dogging are far from 100% predictable from the meaning and usage of dog, so there's a question about where to draw the boundaries of dog's "word family".

That's from a recent post by Mark Liberman at Language Log. It's about the of people's vocabularies, which is surprisingly difficult to estimate for a variety of reasons. On the one hand, what is a word? On the other hand, however you define it, how do you count them? You can't just ask people to list all the words they know. And then: what counts as knowing a word?
Keeping all that in mind, it seems the educated Americans know between 40K and 70K words.