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Statistics 9-12 / Week 03 / Monday
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Week 03 · Two-Way Tables

Monday

Four piles on a grid of tape
// Sign-up cards sorted two ways at once
⏱ about 20 min

Monday: Four Piles on a Grid of Tape

A stack of 48 sign-up cards sits on the table by the community center door. Comet lays down two strips of tape.

"Two questions per card," she says. "Morning slot or evening slot. Finished the practice loop or stopped early."

Wren sorts. Morning and finished, top left. Morning and stopped, top right. Evening below. Four piles grow on the grid.

"18, 6, 12, 12," Comet counts. "What do you notice?"

"24 morning cards and 24 evening cards," Wren says. "Same size groups. But the piles inside them are not the same."

Nova projects a grid with totals along the edges. "Would you like a hint? Write the totals before you compare anything."

"A two-way table," Wren says. "Every card lands in exactly one cell."

"What can we make?" Comet asks. "A table that shows whether the morning runners finished more often."

Index cards sorted into four piles on a grid of tape while Comet counts and Wren fills a two-way table.

The crew's two-way table

Every count this week is the crew's own made-up tally from Nova's Run Log. Each sign-up card is sorted by two questions at once.

FinishedStoppedTotal
Morning18624
Evening121224
Total301848
The crew's two-way table: morning or evening against finished or stopped, 48 cards in all.

Reading the table

The four inner cells are joint counts. Each one answers both questions at once: morning and finished, evening and stopped, and so on.

The row and column totals are marginal counts. They answer one question only: how many morning cards, how many finished cards.

The grand total, 48, is every card. Check it two ways: 24 + 24 and 30 + 18 both give 48.

A solved problem to study

Here is how Wren builds the table from the four piles and checks it.

  1. Count each pile: 18 morning and finished, 6 morning and stopped, 12 evening and finished, 12 evening and stopped.
  2. Add across each row: morning 18 + 6 = 24, evening 12 + 12 = 24.
  3. Add down each column: finished 18 + 12 = 30, stopped 6 + 12 = 18.
  4. Add the row totals and the column totals separately. Both give 48, so the table checks.
COUNT THE CARDS
  • Read the question.
  • Tap your answer.
A two-way table: rows Morning and Evening, columns Finished and Stopped, counts 18 and 6; 12 and 12, total 48.How many sign-up cards are both morning and finished?
How many sign-up cards are evening cards in all?
How many sign-up cards say finished, morning or evening?
How many sign-up cards are there in all?
NAME THE COUNT
  • Read the question.
  • Tap your answer.
The cell with 18 morning-and-finished cards is which kind of count?
The 24 in the morning row total is which kind of count?
The 48 in the corner is which kind of count?
How many sign-up cards are evening and stopped? Type the number.
WHY THIS EXERCISEEvery "and" count is one inner cell. Finding it fast is the first table skill.
StatementTrue or false?
Every sign-up card lands in exactly one inner cell of the table.?
18 + 6 + 12 + 12 = 48?
A row total is a joint count.?
30 + 18 = 24 + 24?
WHY THIS EXERCISEA table that checks two ways has no card lost or counted twice.
Try it
On an index card, copy the crew's table with its totals. Shade the morning row in one color and the finished column in another.
The cell with both colors is the morning-and-finished count.

A table that checks. Tomorrow you turn every count into a percent, three different ways.