your question is interesting but I am not very clear about your purpose. But below, I will talk about my own ideas.
In Chinese, words (詞) are make up with single character （字）。 We can sort them by the sum of single character。
Actually, lots of words only use one character many years ago, which is traditional Chinese language. But in 1919 New Culture Movement (新文化運動) happened, students find new ideas and western culture like democracy and science are hard to spread in common Chinese people using these old language style because they are hard to understand. So they try to replace many single character words with 2(or maybe more)-characters word in order to make the Chinese language closer to daily speaking and make more people accept their ideas.
So modern Chinese has more 2-characters than ever before, so I believe the percentage of it will be more higher than your expect, and 1-characters will be lower. I am unable to give exact numbers(we do not know what is common, what is the define of it), just count words in your vocabulary if your need one.