5.0 Unit 5 Overview: Sampling Distributions

What Is A Sampling Distribution?

A sampling distribution is a distribution where we take ALL possible samples of a given size and put them together as a data set.

For example, let's say we are looking at average number of snap peas taken from a field. If we take all possible samples of size 30 and average those together, we would get a REALLY good picture of what the population average was (which is likely hard to actually calculate). Sampling distributions are important because they lead the way to statistical inference.

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Sampling Distribution for Proportions

For a sampling distribution for proportions, we take the average of all of our possible samples and apply that as the center (mean) of our distribution. Our standard deviation is found using a formula given on the reference page. Once you have those two things, you are well on your way to calculating probabilities for our population proportion.

Sampling Distribution for Means

When dealing with means, our center is the average of all of our sample means. In other words, it's the average of the averages. Our standard deviation is found by dividing our population standard deviation by the square root of our sample size. As our sample size increases, our standard deviation decreases, which plays a huge part in why a large sample size is necessary in performing experiments with quantitative variables.

Sampling Distributions for the Differences in Means and Proportions

The last type of sampling distribution we encounter is when we are seeing if there is a difference in two populations. In this type of sampling distribution, our center is the difference in our two samples (which is presumably 0 if the two populations are not different). This plays a huge part in statistical inference when checking if two populations are in fact different, which is essential in experimental studies.

🎥Watch: AP Stats - Sampling Distributions for Means

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