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Statistics 9-12 / Week 06 / Track Day
6/6
Week 06 · Samples, Surveys and Studies

Track Day

Track Day: a sample from the shelf
// Asking a few runners about the course
⏱ about 20 min

Track Day: A Sample From the Shelf

"Here is our population," Comet says, pointing at a shelf of books. "Every book on it."

"Question: does the book have a picture on its cover?" Wren says. "Checking all of them would take a while."

"So we sample," Comet says. She numbers the books on sticky notes and drops matching scraps in a cup.

"Draw eight," Wren says. Someone draws without looking. The family pulls out the eight books and checks each cover.

"Five of eight," Comet says. "So about five in eight of the whole shelf, give or take. What do you notice?"

Nova glows a row of book spines with eight lit. "Would you like a hint? Now check the whole shelf and compare."

"The parameter against the statistic," Wren says. "Our own little lab."

  1. Population and sample. Parameter and statistic. The sample statistic estimates the population parameter.
  2. Random selection gives every member the same chance. Number, token, shake, draw, match.
  3. Statistics wobble from sample to sample but center near the parameter.
  4. Survey, experiment, observational study: ask where the chance is. Only an experiment can show a cause.
  5. Convenience, voluntary response and leading questions make a report lean. Ask the five questions.
◇ FAMILY RANDOM SAMPLE
Pick a population at home: the books on one shelf, the socks in one drawer, the mugs in one cupboard.
Agree on one yes-or-no question about each member, like "has a picture on the cover".
Number every member and put matching paper scraps in a cup. Draw eight without looking.
Check the eight and find the percent that are yes. That is your statistic.
Then check the whole population. Compare the parameter with your statistic and talk about the gap.
For a grown-up
Any walking or jogging is on a safe path, never a road, with you aware and water at hand.
Help with reaching high shelves. Nothing heavy is lifted alone.
Ask your learner why the cup, and not a person, should do the picking. That answer is the week.
ONE MORE SAMPLE
  • Read the question.
  • Tap your answer.
The family's sample found 5 of 8 books with a cover picture. What percent is that? (Round to 1 place.)
The family checked the whole shelf and found the true percent of books with a cover picture. Is that number a parameter or a statistic?
In a simple random sample, who or what does the picking? Type chance or person.
WHY THIS EXERCISELetting chance pick is what keeps a sample fair for the whole population.
Draw your shelf as a row of rectangles. Shade the eight the cup picked and mark the yes ones.

A fair family sample. Next week the pacing trial: a coin, a model, and whether five tails in a row is surprising.

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