Systematic Errors and the Chappaquiddick Accident

A common procedure when conducting physics experiments is to repeat a measurement several times to calculate the mean and standard deviation. That might be the only instruction we give to students as a means to minimize random errors. However, that technique does not guarantee that the answer will be correct. It might give the same wrong answer every time. How then can we teach students to avoid systematic errors? We don't focus on that problem enough when teaching physics. Part of the problem is that we and the students usually know the correct answers in advance, since student experiments have usually been repeated thousands of times by others.