Sampling Distributions

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As we saw in the last example, each time we sample from a population, we still get a slightly different sample mean. In order to understand how much variation we can expect in those sample means, we can do the following:

• Take a bunch of random samples of fish, each of the same size (50 fish in this example)
• Calculate the sample mean for each one
• Plot a histogram of all the sample means

This process gives us an estimate of the sampling distribution of the mean for a sample size of 50 fish.

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Note that we can look at a sampling distribution for any statistic. For example, we could estimate the sampling distribution of the maximum by calculating the maximum of each sample, rather than the mean (as shown above).

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Let's estimate the sampling distribution of the mean using a population of cod fish. As we did with salmon fish, we will pretend we are all-knowing and have captured weight data on every cod fish in the ocean.

We've set the sample size equal to 50 and created a for loop to take 500 random samples.

• Inside the for loop, use the function np.mean() to calculate the mean of each sample. Save this to a variable called this_sample_mean.
• Then, still inside the for loop, append this_sample_mean to the list sample_means and run the simulation.