Mistake Master · AP Statistics · Unit 1 · Step-Through Animation
The Number You Computed Is Not the Number You Were Asking About
You'll learnto keep the measured group and the group in question apart: which number is the statistic, which is the parameter, why they differ, and why a bigger badly chosen sample never closes the gap.
A city has 200 registered voters and a real, fixed answer to the question "what share of them support the incumbent?" — but nobody can see it. A poll can only measure 25 of them. This animation builds that city, draws that sample, and counts: 13 of the 25 support her, so the poll's number is 52 percent while the city's number is 44. Neither is a mistake. Then it draws the sample 40 more times to show the poll's number moving while the city's does not, and finishes on the one repair that does not work — sampling more people from the wrong place, which converges beautifully on the wrong answer.
8 STEPS · 6 QUICK CHECKS · POPULATION vs SAMPLE · PARAMETER vs STATISTIC · SAMPLING VARIATION · BIAS · v1
p = 44% fixed and unseen · p-hat = 52% measured · one is an estimate of the other
Before you start
What you're looking at
200 circles, one per registered voter in a small city. A circle is hollow until it is measured; measuring it shows whether that voter supports the incumbent.
The question
What share of all 200 support her — and what exactly has a poll of 25 of them told you about it?
Watch for
The 8-point gap between the poll's 52% and the city's 44%, the 40 repeat samples spreading around a line that never moves, and the biased sample that gets more precise about the wrong group.
Mistake Master