9th grade · Math · Unit 16 of 22
Two-Way Tables & Causation
Relative frequency and correlation
What your child practices
Reading two-way frequency tables, finding conditional relative frequencies, spotting associations, and knowing that correlation does not prove causation.
New York State Learning Standards learning standard: AI-S.ID.5; AI-S.ID.9 · two-way tables, relative frequency, and correlation versus causation
How we explain it
Children can open this short lesson before they practice.
- A joint frequency is one cell. A row total is a marginal frequency.
- A conditional percent is a cell ÷ its row total.
- Two things changing together does not prove one causes the other.
Example: Of 40 students who ate breakfast, 30 felt rested. What percent is that? 30 ÷ 40 = 0.75. Answer: 75%
Two-Way Tables & Causation in New York
In the New York State Learning Standards, this is unit 16 of 22 in 9th grade Math, after Rearranging Formulas and before Sequences.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
How many in the "Doesn't like reading" row are in the "No library card" column?
Reading survey Has a library card No library card Total Likes reading 34 6 40 Doesn't like reading 31 9 40 Total 65 15 80 - 31
- 6
- 40
- 9
9
Hint: Find the row, then move across to the column.
Question 2
Cities with more firefighters have more fires. What is the best conclusion?
- They are linked, but this does not prove one causes the other. Bigger cities have both more firefighters and more fires.
- One must cause the other
- The data must be wrong
- There is no link at all
They are linked, but this does not prove one causes the other. Bigger cities have both more firefighters and more fires.
Hint: Correlation shows two things change together. It does not prove that one causes the other.
Question 3
What percent of the "Ate breakfast" row are "Felt rested"?
Morning survey Felt rested Felt tired Total Ate breakfast 10 30 40 No breakfast 19 6 25 Total 29 36 65 - 25%
- 34.5%
- 35%
- 15.4%
25%
Hint: 10 out of 40 = 10 ÷ 40 × 100.
Question 4
Compare the percent of each row that is "Felt rested". Is there evidence of an association?
Morning survey Felt rested Felt tired Total Ate breakfast 19 31 50 No breakfast 21 4 25 Total 40 35 75 - Yes, the percents are very different
- Not much, the percents are close
- You can't tell from a two-way table
Yes, the percents are very different
Hint: Ate breakfast: 38%. No breakfast: 84%.
Question 5
How many in the "Grade 9" row are in the "Rides to school" column?
Getting to school Walks to school Rides to school Total Grade 8 18 7 25 Grade 9 20 20 40 Total 38 27 65 - 7
- 18
- 40
- 20
20
Hint: Find the row, then move across to the column.
Question 6
Students who own more books tend to have higher reading scores. What is the best conclusion?
- There is no link at all
- They are linked, but this does not prove one causes the other. Something else, like time spent reading at home, could explain both.
- One must cause the other
- The data must be wrong
They are linked, but this does not prove one causes the other. Something else, like time spent reading at home, could explain both.
Hint: Correlation shows two things change together. It does not prove that one causes the other.