9th grade · Math · Unit 15 of 18
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.
Alabama Course of Study content standard: GDA.14; AIP.35 · 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 Alabama
In the Alabama Course of Study, this is unit 15 of 18 in 9th grade Math, after Statistics in Society and before Function Notation.
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 36 4 40 Doesn't like reading 5 20 25 Total 41 24 65 - 5
- 4
- 25
- 20
20
Hint: Find the row, then move across to the column.
Question 2
Cities with more firefighters have more fires. What is the best conclusion?
- 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.
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 "Plays sports" row are "Has a pet"?
Sports and pets Has a pet No pet Total Plays sports 4 21 25 No sports 22 3 25 Total 26 24 50 - 15.4%
- 26%
- 16%
- 8%
16%
Hint: 4 out of 25 = 4 ÷ 25 × 100.
Question 4
Compare the percent of each row that is "Has a library card". Is there evidence of an association?
Reading survey Has a library card No library card Total Likes reading 7 33 40 Doesn't like reading 2 23 25 Total 9 56 65 - You can't tell from a two-way table
- Not much, the percents are close
- Yes, the percents are very different
Not much, the percents are close
Hint: Likes reading: 18%. Doesn't like reading: 8%.
Question 5
Students who own more books tend to have higher reading scores. What is the best conclusion?
- They are linked, but this does not prove one causes the other. Something else, like time spent reading at home, could explain both.
- There is no link at all
- 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.
Question 6
What percent of the "Likes reading" row are "Has a library card"?
Reading survey Has a library card No library card Total Likes reading 9 11 20 Doesn't like reading 15 35 50 Total 24 46 70 - 12.9%
- 37.5%
- 45%
- 55%
45%
Hint: 9 out of 20 = 9 ÷ 20 × 100.