Trial and error is a form of problem solving therefore it doesn't really fit in with analysis of data. When it comes to analysis though it is often an iterative process, before we come up with something we think is reasonable. So on that basis trial and error is a way of getting to a conclusion.
Something I found all too often and found quite depressing as a teacher is just getting some kids to try, give it a go. Once they have come up with something, they can then form an opinion on their conclusion. They should then be encouraged to figure out what is right or wrong about their suppositions.
By going round the loop a few times, they can develop a better understanding of the problem and subsequently a solution. Like training to run it is sometimes that first step out of the door that leads to greater things.
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