The Sampling Distribution

Part of the Statistics for ML section of Coddy's Machine Learning journey. Lesson 21 of 64.

Video sessions are right-skewed: most last a few minutes, a few run two hours. Yet the means of 1000 samples of 40 sessions form a bell:

Two histograms on one chart. Single sessions in gray pile up near 0 minutes with a long tail to 120. The means of 40 sessions form a narrow blue bell around the population mean of 30 minutes

The histogram of many sample means is the sampling distribution. With enough values in each sample, it is a bell centered on the population mean, even for skewed data:

means = sample_means(sessions, 40, 1000)  # your function from Sample Means Vary
ax.hist(means, bins=12)

That is the central limit theorem. It makes averages predictable: a model's mean error over a test set is roughly normal too.

Challenge

Medium

A cloud drive's 6000 file sizes in files (MB) are right-skewed: many documents, a few videos. The program reads a sample size; the starter has sample_means and two charts.

Get 500 sample means of that size.
Print mean minus median for the files, then the means (2 decimals).
Histogram the files on axs[0] and the means on axs[1], bins=12, and show.

For another drive and 60:

Files: mean - median = 25.28 MB
Sample means: mean - median = 0.55 MB

Two histograms side by side. All Files: a tall first bar and a long thin tail to the right. Sample Means: a symmetric bell

Then Coddy reports each chart. A gap near 0 means the skew is gone.

Try it yourself

import numpy as np
import matplotlib.pyplot as plt

size = int(input())

# Don't change the lines below: the size in MB of every file in the drive
rng = np.random.default_rng(21)
files = np.round(rng.random(6000) ** 4 * 300 + 5, 2)


# Your function from Sample Means Vary: the means of count samples
def sample_means(data, size, count):
    means = []
    for i in range(count):
        sample = rng.choice(data, size=size, replace=False)
        means.append(sample.mean())
    return np.array(means)


fig, axs = plt.subplots(1, 2)
axs[0].set_title("All Files")
axs[0].set_xlabel("File size (MB)")
axs[1].set_title("Sample Means")
axs[1].set_xlabel("Mean file size (MB)")

# Write your code below