I am writing a report on statistics and data analysis. For some experiments I created intentionally some data which is not directly related to real world phenomena. Which term is correct to describe such data: artificial data or synthetic data? Is the data artificially created or synthetically created? Or are both adjectives synonyms?
This is often called 'test data'
Test data is data which has been specifically identified for use in tests, typically of a computer program.
That term is understood to mean data that has been created, synthesised, anonymised from "real" data, or is a copy or version of real data, to be used for the purposes of exercising a computer system in a non-production environment. As suggested in a comment by Robusto, "dummy data" also has this meaning.
You should call this "dummy data" or "test data." The terms artificial data and synthetic data are actually used for data that is constructed to be similar to real data but that manipulated such that the underlying real world items cannot be identified.
For example, the US Census Bureau is now creating synthetic data for its Survey of Income and Program Participation. The data are designed to be provide detailed information on household incomes and participation in federal benefit programs, without compromising the privacy of individual participants.