S23 — The cloud and the histogram are the same cloud

Lesson 4 built a cloud of slopes by resampling data. Lesson 10 built a histogram of allele frequencies by random copying. They look like different pictures from different units. They are the same object: a sampling distribution, and both tighten at the same rate, 1/√n. Set the sample size once and watch the two collapse together. ← all activities

Predict first. As you raise the sample size n, the slope cloud (left) and the allele-frequency histogram (right) will:

Sample size — shared by both

30

Lesson 4 — bootstrap slope cloud

SD of the slope: —

Lesson 10 — Wright–Fisher p′ histogram

SD of p′: —

Both spreads versus 1/√n

Each curve is a sampling-distribution width as n grows. The dashed reference is proportional to 1/√n. Two different machines, one law.