How do we know that truly random samples accurately represent general populations?
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The Law of Large Numbers. It’s not just an expression. It’s an actual mathematical result. It tells us that the average of a random sample tends towards the average in the population. This is supported both by probability theory and by any number of experiments where the average in the population was already known and the sample did a good job of estimating it.
Even more remarkably, the LLN tells us, for a given sample size, how much we could potentially be off. This is how statisticians calculate things like the margin of error.
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