9th grade · Math · Unit 16 of 17
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.
Alaska content standards learning standard: S-ID.5; S-ID.9 · two-way tables, conditional 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 Alaska
In the Alaska content standards, this is unit 16 of 17 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.
Source: Alaska Department of Education and Early Development
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
Cities with more firefighters have more fires. What is the best conclusion?
- There is no link at all
- One must cause the other
- They are linked, but this does not prove one causes the other. Bigger cities have both more firefighters and more fires.
- The data must be wrong
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 2
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 12 38 50 Grade 9 10 10 20 Total 22 48 70 - 38
- 20
- 10
- 7
10
Hint: Find the row, then move across to the column.
Question 3
Compare the percent of each row that is "Walks to school". Is there evidence of an association?
Getting to school Walks to school Rides to school Total Grade 8 15 10 25 Grade 9 12 13 25 Total 27 23 50 - Not much, the percents are close
- Yes, the percents are very different
- You can't tell from a two-way table
Not much, the percents are close
Hint: Grade 8: 60%. Grade 9: 48%.
Question 4
What percent of the "Plays sports" row are "Has a pet"?
Sports and pets Has a pet No pet Total Plays sports 19 21 40 No sports 18 2 20 Total 37 23 60 - 51.4%
- 31.7%
- 57.5%
- 47.5%
47.5%
Hint: 19 out of 40 = 19 ÷ 40 × 100.
Question 5
What percent of the "Likes reading" row are "Has a library card"?
Reading survey Has a library card No library card Total Likes reading 28 22 50 Doesn't like reading 9 16 25 Total 37 38 75 - 37.3%
- 56%
- 66%
- 75.7%
56%
Hint: 28 out of 50 = 28 ÷ 50 × 100.
Question 6
Compare the percent of each row that is "Walks to school". Is there evidence of an association?
Getting to school Walks to school Rides to school Total Grade 8 23 2 25 Grade 9 34 6 40 Total 57 8 65 - Yes, the percents are very different
- You can't tell from a two-way table
- Not much, the percents are close
Not much, the percents are close
Hint: Grade 8: 92%. Grade 9: 85%.