Now, if we draw an adult male at random from the population, then we expect his height to be around the population average mu, give or take about one standard deviation sigma. After all, the standard deviation sigma measures the spread of the population. And most observations are around one standard deviation away from the mean mu. We say that the expected value of one random draw is the population average mu. Now, how about the average of n draws, which we call x bar, with a subscript n? So the subscript stands for the sample size. So, it turns out that the expected value of the sample average is, again, the population average mu. But keep in mind that the sample average is actually random, because sampling is a random process. That means that x bar won't be exactly equal to the population mean, which is actually 69.3 inches. For example, we might get x bar equal to 70.1 inches. And if we take another sample of size n, we might get x bar equal to 69.1 inches. So then the question is, how far off from the population mean will the sample mean be? This is determined by the standard error, or SE. This is a very important quantity in statistics, and it tells you roughly how far off the statistic will be from an expected value. The standard error for a statistic is used for all kinds of statistical procedures. The standard error of a statistic plays the same role that the standard deviation sigma plays for one observation drawn at random, because it's a give or take number that shows how far off we expect the statistic to be from the mean. So, here's one of the key facts for a statistical inference, it's called the square root law. It says that, "the standard error of the sample average, equals sigma, divided by square root of sample size". Why is the square root law so important? There are actually two reasons for that. First, it shows that the standard error becomes smaller if we use a larger sample size n. After all, there's a square root in the denominator. We can actually use that formula to determine what sample size is required to get a desired accuracy for our standard error. The second point is that the formula does not depend on the size of the population, only on the size of the sample. This is the reason why statistics works in polls. After all, remember our previous example, where we looked at 140 million adult men. It doesn't really matter that we look at 140 million. If we take a sample of size 1,000, we get a certain standard error, no matter how large the population is.