Two-Way Tables · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Two-Way Tables

Mathematics · Data & Statistics · ages 12-14
Name ______________________   Date ____________

  1. Look at this table:

    Plays sportNo sportTotal
    Has a pet18624
    No pet101626
    Total282250

    How many students in total do NOT play a sport?

    • 22
    • 6
    • 16

  2. Using the finished table (18 pet owners play a sport, 12 do not; 9 non-pet owners play a sport, 21 do not), how many students both have a pet AND play a sport?

    Answer: ______________

  3. Using the same six kids (Amy, Ben, Cara, Dan, Ella, Finn) from before, how many kids ride to school?

    Answer: ______________

  4. Look at this table:

    Plays sportNo sportTotal
    Has a pet18624
    No pet101626
    Total282250

    How many students have a pet AND play a sport?

    • 6
    • 18
    • 24

  5. In the pet and sport table, 18 out of 30 pet owners play a sport. Only 9 out of 30 non-pet owners play a sport. Which group has the higher rate of playing sports?

    • Pet owners
    • Non-pet owners
    • Both are exactly the same

  6. In a two-way table, 75% of pet owners play a sport, but only about 38% of non-pet owners do. What does this suggest?

    • Pet ownership and playing a sport seem linked
    • Pet ownership and playing a sport are not related at all
    • The table must have a mistake since the percentages differ

  7. A coach made this table about 60 students:

    | | Plays a sport | No sport | Total | |---|---|---|---| | Has a pet | ? | 12 | 30 | | No pet | 9 | 21 | 30 | | Total | 27 | 33 | 60 |

    What number belongs in the blank cell (pet owners who play a sport)?

    Answer: ______________

  8. Six students were asked if they walk to school and if they pack lunch: Ava - walks, packs lunch Ben - walks, buys lunch Cleo - rides, packs lunch Dan - walks, packs lunch Eva - rides, buys lunch Fin - rides, packs lunch

    How many students walk to school AND pack lunch?

    • 1
    • 2
    • 3

  9. What fraction of pet owners play a sport? 18 out of 30 pet owners play a sport. Give your answer as a decimal.

    Answer: ______________

  10. Kai looks at a two-way table with 24 pet owners and 26 non-owners. He says: '18 pet owners play sport, but only 10 non-owners do, so pet owners are way more into sport.' What's wrong with Kai's reasoning?

    • Kai's reasoning is completely correct
    • Kai should have compared row totals instead
    • Kai compared raw counts, but the groups are different sizes, so percentages would be fairer
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Two-Way Tables W1-mt_oD1Rgg52n3-s1

  1. 22 · Add the 'No sport' column: 6 + 16 = 22. You can also just read the 'No sport' total at the bottom.
  2. 18 · That's the joint frequency sitting right in the 'pet owner, plays sport' cell.
  3. 3 · Cara, Dan, and Finn all ride to school.
  4. 18 · Find the row 'Has a pet' and the column 'Plays sport'. They meet at 18.
  5. Pet owners · 18 out of 30 is 60%, but 9 out of 30 is only 30%, so pet owners play sports at a higher rate.
  6. Pet ownership and playing a sport seem linked · When relative frequencies differ a lot between groups, the two categories look connected.
  7. 18 · The pet-owner row has to add up to 30, and 12 already play no sport, so 18 must play a sport.
  8. 2 · Ava and Dan both walk and pack lunch. That's 2 students.
  9. 0.6 · 18 divided by 30 gives the decimal form of that relative frequency.
  10. Kai compared raw counts, but the groups are different sizes, so percentages would be fairer · 24 and 26 are close here, but raw counts can mislead when group sizes differ. Percentages account for group size.
Worksheet · LightMySky