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Statistics is a tool to make sense of large amounts of information. Common sense can only handle limited amounts of information. Until recently common sense was sufficient for most people because daily life didn't involve processing a large amount of data. Now large stores of information have become readily available. You can either choose to ignore the information available or you can choose to make sense of it, which means learning statistics.
Most people think statistics is boring and difficult. Statistics is to data, what grammar is to words. And like grammar, it's only interesting if it's used to understand something interesting.
In Stat 100, we use statistics to research a topic we're all interested in - ourselves. We collect data on ourselves through anonymous surveys, largely on the sort of social questions on which students have shown intense interest. Having real questions that we want to answer motivates real understanding, not just memorizing some complicated rules. Statistics is a collection of real tools- the key is to understand which one to use when and why.
Read the newspaper in a new way, without their eyes glazing over when they see quantitative information.
Know what questions to ask in evaluating studies and surveys.
Understand what questions can and cannot be answered by statistical arguments.
Appreciate how much of what matters to them can be better understood with statistics.
Feel much more confident applying both logical reasoning and common sense to quantitative topics but are very aware that their intuition can sometimes be so wrong that it's shocking.
But what's most surprising is they actually like statistics!