These statistics supposedly come from Albert Mehrabian's book "Silent Messages: Implicit Communication of Emotions and Attitudes," a book about nonverbal communication and body language.

However, Mehrabian's research is, most of the time, misunderstood and misinterpreted.

"Please note that this and other equations regarding relative importance of verbal and nonverbal messages were derived from experiments dealing with communications of feelings and attitudes (i.e., like-dislike). Unless a communicator is talking about their feelings or attitudes, these equations are not applicable. Also see references 286 and 305 in Silent Messages -- these are the original sources of my findings."

Here's an article by Dr. Judith E. Pearson, explaining in more detail how this research has been misused.