Should fact based be hyphnated?

Yes.

The professor presented fact-based data.

To determine if "fact based" should be hyphenated, you can consult a dictionary or a style guide. The general rule is that when a compound modifier comes before a noun, it should be hyphenated to clarify its meaning.

In this case, "fact based" is a compound modifier that describes the noun it precedes. "Fact" modifies "based" to specify that the basis of something is factual. Therefore, it would be appropriate to hyphenate it as "fact-based" when using it as an adjective before a noun.

For example:
- "She conducted a fact-based study on climate change."
- "The movie is a well-researched, fact-based portrayal of historical events."

However, if you are using "fact based" after a verb or a subject, it is not necessary to hyphenate it.

For example:
- "Her study is based on facts." (no hyphenation needed)
- "The decision was fact based." (no hyphenation needed)

Remember, it's always a good idea to consult the specific style guide or dictionary you are working with, as different style guides may have slight variations in their rules for hyphenation.