Mistake Master · AP Statistics · Unit 1 · Step-Through Animation
Twice as Many Walkers, Half as Many Walkers
You'll learnto build a frequency and a relative frequency table, and to see why only the second one can compare two groups of different sizes.
Northgate has 300 students who walk to school. Riverside has 150. Twice as many walkers at Northgate — and Riverside is the school where walking is common, at 30 percent against 15. Both sentences are true, because Northgate has four times as many students. This animation builds the frequency table for both schools, divides every count by its own total, and reads the two tables side by side: two rows where the counts and the shares disagree outright, one row where they agree, and one row with four times the count at exactly the same share. Then it divides by the wrong total, and watches the wrong answer come back.
8 STEPS · 6 QUICK CHECKS · FREQUENCY TABLE · RELATIVE FREQUENCY · UNEQUAL GROUPS · THE DENOMINATOR · v1
300 walkers vs 150 · 15% vs 30% · the counts and the shares disagree
Before you start
What you're looking at
Two schools of very different sizes — Northgate 2,000 students, Riverside 500 — and how each school's students get to school.
The question
Which school walks more? The counts and the percentages give different answers, and only one of them is answering the question.
Watch for
The two rows that reverse, the one row that does not, the car row with 4x the count at the same share, and the wrong denominator putting the wrong answer back.
Mistake Master