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9th grade · Math · Unit 16 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.

California 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.

  1. A joint frequency is one cell. A row total is a marginal frequency.
  2. A conditional percent is a cell ÷ its row total.
  3. 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%

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    People who carry umbrellas are more likely to have wet shoes. What is the best conclusion?

    • They are linked, but this does not prove one causes the other. Rainy weather could cause both.
    • The data must be wrong
    • One must cause the other
    • There is no link at all

  2. Question 2

    How many in the "Doesn't like reading" row are in the "No library card" column?

    Reading survey
    Has a library cardNo library cardTotal
    Likes reading172340
    Doesn't like reading47350
    Total642690
    • 23
    • 3
    • 47
    • 50

  3. Question 3

    What percent of the "Plays sports" row are "Has a pet"?

    Sports and pets
    Has a petNo petTotal
    Plays sports91625
    No sports133750
    Total225375
    • 12%
    • 40.9%
    • 36%
    • 46%

  4. Question 4

    Compare the percent of each row that is "Walks to school". Is there evidence of an association?

    Getting to school
    Walks to schoolRides to schoolTotal
    Grade 824850
    Grade 921425
    Total235275
    • Yes, the percents are very different
    • You can't tell from a two-way table
    • Not much, the percents are close

  5. Question 5

    Cities with more firefighters have more fires. What is the best conclusion?

    • The data must be wrong
    • 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.
    • There is no link at all

  6. Question 6

    What percent of the "Likes reading" row are "Has a library card"?

    Reading survey
    Has a library cardNo library cardTotal
    Likes reading291140
    Doesn't like reading16925
    Total452065
    • 44.6%
    • 64.4%
    • 82.5%
    • 72.5%

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