Mathematical Methods · sample proportions · manipulative

Building the distribution of p̂

p̂ only lands on multiples of 1/n. Extreme p keeps the mound skewed until n is large — that is what differs from the sample-mean twin.

population (0 / 1) latest sample p̂ values p (theory) mean of p̂

Population — Bernoulli(p)

Distribution of sample proportions p̂

Draw a sample — red highlights the n outcomes on top; p̂ appears below

0.50
1
20

Last sample: –

Theory

Samples collected

trials
0
mean of p̂
–
sd of p̂ (observed)
–
√p(1−p)/n (theory)
–