![]() Then when you take the average of all those sample means they should even out to be equal to the population mean, this is known as the central limit theorem. Thus, each sample from the population should have a mean pretty close to the population mean. ![]() if you take a sample from the population, you will more than likely get individual values around the population average. The mean is the average value of all the members of the population. It's really important to be clear on the difference between your population and your samples. When constructing the sampling distribution of the sample mean you are taking a bunch of different samples from the population and calculating their means. Completely ignoring the possibility of closed form mathematical solutions is important to get clear about this. Consequently it is likely that yours does too.įor intuition it is important to think about how you could learn about variability by aggregating sampled information that is generated in various ways and on various assumptions. This is a reasonable thing to do because not only is the sample you have the best, indeed the only information you have about what the population actually looks like, but also because most samples will, if they're randomly chosen, look quite like the population they came from. If, for example, students are learning about the sampling distribution. Sampling 'with replacement' is just a convenient way to treat the sample like it's a population and to sample from it in a way that reflects its shape. features in Lanes online textbook, including the Java Applets, the textbook. You can do this because the sample you have is also a population, just a very small discrete one it looks like the histogram of your data. An alternative is to take the sample you have and sample from it instead. This seems like a good idea provided you are happy to make the assumptions. (Indeed particularly convenient assumptions plus non-trivial math may allow you to bypass the sampling part altogether, but we will deliberately ignore that here.) That would be straightforward to the extent that you chose computationally convenient assumptions. Following the previous strategy you could again learn about how much the answer to your question when asked of a sample might vary depending on which particular sample you happened to get by repeatedly generating samples of the same size as the one you have and asking them the same question. that it is Normal, or Bernoulli or some other convenient fiction. Imagine you decide to make assumptions, e.g. Since this isn't possible you can either make some assumptions about the shape of the population, or you can use the information in the sample you actually have to learn about it. One way you might learn about this is to take samples from the population again and again, ask them the question, and see how variable the sample answers tended to be. Now, how confident you should be that the sample answer is close to the population answer obviously depends on the structure of population. So you take a sample and ask the question of it instead. You want to ask a question of a population but you can't. This StackExchange post is the best explanation I've come across so far: I believe OP is referring to bootstrapping, or more generally, resampling.
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