@Stephen - the sample size is indeed a concern, but there shouldn't be this much deviation with the amount of text we had (we analyzed all of the english-learning articles for the last year). The "the" issue is curious though, because it is relatively rare for a language to have a non-gender version of a word that functions as "the" does. Many languages don't have the word at all.

Thank you. Very interesting. I`ve just finished my deck for Anki based on words graded according to zipf law. I have 14000 the most frequent words in English.

Very interesting article, Ivan.  Thank you! 

Maybe you just needed a bigger sample of English to square your own data with that expected by Zipf’s Law.