On various occasions (most recently today in an email message), I have heard it said that, "The plural of anecdote is not data." Curious as to where this originated, I did a quick web search using my search engine of choice. Some, like the Quotes About Data Processing website attribute the statement to Frank Kotsonis. Others, like the source of the above image, credit Roger Brinner. Others claim that the original statement was the opposite, i.e. "The plural of anecdote IS data." by Raymond Wolfinger. Two implications (of the original statement) found at the previous link are: 1) data is usually collected in the first place because anecdotal evidence flagged something as worthy of investigation, and 2) the idea that data alone can prove something as true, while anecdotes cannot is absurd. Neither data nor anecdotes prove anything. Scientific theories are never, ever, ever proven. They can only be disproven.
In looking around online, I found that others have similarly spent time wondering about and even blogging on this topic. Check out Skeptical Medicine for one such example.