Tuesday
Tuesday: Three Kinds of Percent
"18 morning runners finished," Comet says. "Is that a lot? 18 out of what?"
"That is the whole question," Wren says. "Out of all 48 cards, it is 37.5%. Out of the 24 morning cards, it is 75%."
"Two percentages from one cell," Comet says. "And the 24 morning cards out of 48 is 50%. Three percentages."
Nova shows three tables with different cells lit. "Would you like a hint? Each percent has a different number underneath."
"Joint: cell over everything," Wren says. "Marginal: edge total over everything. Conditional: cell over its own row."
"Then evening finished is 12 of 24," Comet says. "50%. The morning runners finished more often. What do you notice?"
"A gap of 25 points," Wren says. "That is worth a closer look."
Way 1: percentages of everything
A joint relative frequency is one cell over the grand total. Morning and finished: 18 ÷ 48 = 37.5%.
A marginal relative frequency is an edge total over the grand total. Morning: 24 ÷ 48 = 50%. Finished: 30 ÷ 48 = 62.5%.
Both kinds use every card as the whole. They tell you the share of all cards.
Way 2: percentages inside one group
A conditional relative frequency is a cell over its own row or column total. Finished given morning: 18 ÷ 24 = 75%.
Finished given evening: 12 ÷ 24 = 50%. Each row is its own whole, so the rows can be compared fairly.
Turn it around and the whole changes. Morning given finished: 18 ÷ 30 = 60%. Same cell, different total.
| Finished | Stopped | Total | |
|---|---|---|---|
| Morning | 75% | 25% | 100% |
| Evening | 50% | 50% | 100% |
This is the row-percent table. Each row adds to 100%, and the finished column shows 75% against 50%.
| Percent | Count | Total used | Result | Kind |
|---|---|---|---|---|
| Morning and finished, of all cards | 18 | 48 (everyone) | 37.5% | joint |
| Morning, of all cards | 24 | 48 (everyone) | 50% | marginal |
| Finished, among morning cards | 18 | 24 (morning row) | 75% | conditional |
| Morning, among finished cards | 18 | 30 (finished column) | 60% | conditional |
- Read the question.
- Tap your answer.
Of all 48 sign-up cards, what percent are both morning and finished? (Round to 1 place.)Of all 48 sign-up cards, what percent say finished? (Round to 1 place.)Among the 24 morning cards, what percent say finished? (Round to 1 place.)Among the 24 evening cards, what percent say finished? (Round to 1 place.)- Read the question.
- Tap your answer.
| Statement | True or false? |
|---|---|
| 18 ÷ 24 = 0.75 | ? |
| A conditional percent uses the grand total underneath. | ? |
| Each row of a row-percent table adds to 100%. | ? |
| "Finished given morning" and "morning given finished" always give the same percent. | ? |
Then cover the stopped column and read "morning given finished" the same way.
Three percentages from one table. Tomorrow is Data Lab: build your own table from 24 cards and two coins.