The purpose of this lesson is for students to understand that random samples produce different estimates for population characteristics, and for students to understand the concept of using the margin of error to estimate a population characteristic from a sample statistic. To get a sense of how a statistic might vary from sample to sample, we can imagine how that statistic might be measured from many random samples of the sample size, or from a sampling distribution. One way to imagine a sampling distribution is to treat an initial sample as representative of the population, then repeatedly draw samples with replacement from the original sample, and compute the value of a chosen sample statistic, such as the proportion of data that is in a category or the mean of the values in the data. The variability of the sampling distribution model we constructed can be used to find a margin of error.

A margin of error is defined as the maximum expected difference between a point estimate for a population characteristic, obtained from our sample statistic, and the actual value of the population characteristic. When students make connections between standard deviation and margin of error to estimate a plausible interval for a population mean, they are looking for and making use of structure (MP7).