9th grade · Math · Unit 9 of 16
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.
Texas Essential Knowledge and Skills (TEKS) teks student expectation: A.4(B) · association and 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 Texas
In the Texas Essential Knowledge and Skills (TEKS), this is unit 9 of 16 in 9th grade Math, after Data & Scatter Plots and before Polynomials.
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.
Source: Texas Education Agency (TEA)
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 17 8 25 Doesn't like reading 29 21 50 Total 46 29 75 - 21
- 29
- 8
- 50
21
Hint: Find the row, then move across to the column.
Question 2
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 2 18 20 Doesn't like reading 15 10 25 Total 17 28 45 - Not much, the percents are close
- You can't tell from a two-way table
- Yes, the percents are very different
Yes, the percents are very different
Hint: Likes reading: 10%. Doesn't like reading: 60%.
Question 3
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 4
What percent of the "Ate breakfast" row are "Felt rested"?
Morning survey Felt rested Felt tired Total Ate breakfast 15 5 20 No breakfast 12 13 25 Total 27 18 45 - 75%
- 55.6%
- 85%
- 33.3%
75%
Hint: 15 out of 20 = 15 ÷ 20 × 100.
Question 5
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 18 25 Doesn't like reading 19 31 50 Total 26 49 75 - You can't tell from a two-way table
- Yes, the percents are very different
- Not much, the percents are close
Not much, the percents are close
Hint: Likes reading: 28%. Doesn't like reading: 38%.
Question 6
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 4 21 25 Grade 9 10 15 25 Total 14 36 50 - 10
- 21
- 25
- 15
15
Hint: Find the row, then move across to the column.