So far you’ve learned how to appropriately obtain meaningful data, how to make sense of that data through distributions or numerical summaries, and how to determine the probability of seeing certain outcomes.

From now on, we’re going to use sample data to draw conclusions about the larger population from which the sample was taken. If you spend some time thinking about this, it’s pretty cool that we’re going to be able to make some very educated guesses as to a certain characteristic of a population just by looking at a small sample of individuals from that population. We won’t be computing exact values (because that would entail knowing results from the entire population); rather, we’ll be computing a range of possible values for the population. All of our inference methods are based on one extremely important fact: *data varies*. Therefore, we’ll never know for certainty the exact value of a population’s characteristic. But with the methods of inference, we’ll take the variation into account, and create a range of possible values.

Using the idea of the **law of large numbers**, we do know that if we increase the size of our sample, our sample mean *x̄* will get closer and closer to the true, unknown, population mean *μ*. But there is a trade-off: although a larger sample means a more accurate estimate of the population mean, obtaining a larger sample requires more time and money to collect, record, and summarize the data.