Week 05 · Rules or Learning?

Wednesday

Explorer Lab: Let the data pick the cut-off

// Hand-written rules versus patterns found in data

⏱ about 20 min

Wednesday: Explorer Lab: Let the Data Pick the Cut-off

Raven deals ten labeled cards onto the table: five stars and five planets.

"No guessing today," she says. "We test each possible rule on every card and count."

Rocket picks up a pencil. "So the rule that gets the most right wins?"

"That is the idea," Nova says. "Counting over many examples to find a pattern."

"It is a small paper version of statistical inference."

Rocket draws a tally chart with four columns, one for each rule, and Raven reads out the first card.

"Card one: a star, brightness 120, size 2."

You will test four possible rules for telling stars from planets.

For each rule, count how many of the ten labeled cards it gets right.

The best rule is the one the data supports, not the one you guessed.

For a grown-up

Help copy the ten cards, or read the numbers aloud while your explorer tallies.
Every number is invented for the lesson, so answers can be checked.

Card	Label	Brightness	Size
1	star	120	2
2	planet	230	5
3	star	210	3
4	planet	190	4
5	star	60	2
6	planet	240	6
7	star	225	1
8	planet	205	5
9	star	100	3
10	planet	170	4

PREDICT FIRST

Which feature do you predict will separate stars from planets better?

Rule A: if brightness is 200 or more, then planet, else star. Check every card and tally the right answers.
Rule B: if size is 3 or more, then planet, else star. Tally again.
Rule C: if size is 4 or more, then planet, else star. Tally again.
Rule D: if size is 5 or more, then planet, else star. Tally again.
Write each total out of 10 in the results table.

Rule A: right out of 10

Rule B: right out of 10

Rule C: right out of 10

Rule D: right out of 10

Which feature did the best rule use? Type one word.

WHY THIS EXERCISEThe winning cut-off came from the evidence, not from a guess.

Notice what happened. Nobody told you "size 4." The pattern came out of the counting.

This is a tiny, paper stand-in for the idea of learning from data. Real systems need far more examples.

Did your prediction match the result? What surprised you?Card 7 is a very bright star. Why does it fool Rule A?

Superb counting! Tomorrow we compare the learned rule with the hand-written one on Sky Sorter.

Grown-up checked my answers