# Sampling Distributions

Learn how to quantify the statistics of a randomly sampled experiment and visualize the distribution.

Start## Key Concepts

Review core concepts you need to learn to master this subject

Central Limit Theorem

Standard Error & Sample Size

Biased Estimators

CLT & CDF

Central Limit Theorem Assumptions

Standard Error

Central Limit Theorem

Central Limit Theorem

According to the Central Limit Theorem, the sampling distribution of the mean:

- is normally distributed
- has a mean equal to the population mean
- has standard deviation (also called standard error) equal to the population standard deviation divided by the square root of the sample size

In the plots provided, the left plot shows the population distribution of salmon weights, and the right plot shows the sampling distribution of the mean salmon weights.

Sampling Distributions

Lesson 1 of 1

- 1In statistics, we often want to learn about a large population. Since collecting data for an entire population is often impossible, researchers may use a smaller sample of data to try to answer the…
- 2Now that we’ve generated some random samples from a population using an applet, let’s code this ourselves in Python. The numpy.random package has several functions that we could use to simulate ran…
- 3As we saw in the last example, each time we sample from a population, we will get a slightly different sample mean. In order to understand how much variation we can expect in those sample means, we…
- 4So far, we’ve defined the term
*sampling distribution*and shown how we can simulate an approximated sampling distribution for a few different statistics (mean, maximum, variance, etc.). The *Centr… - 5Now that we’ve examined the CLT from a high level, let’s get into the details. The CLT not only establishes that the sampling distribution will be normally distributed, but it also allows us to de…
- 6The second part of the Central Limit Theorem is: The sampling distribution of the mean is normally distributed, with standard deviation equal to the population standard deviation (often denoted …
- 7According to the Central Limit Theorem, the mean of the sampling distribution of the mean is equal to the population mean. This is the case for some, but not all, sampling distributions. Remember, …
- 8Once we know the sampling distribution of the mean, we can also use it to estimate the probability of observing a particular range of sample means, given some information (either known or assumed) …

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