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Statistics 9-12 / Week 06 / Friday
5/6
Week 06 · Samples, Surveys and Studies

Friday

Reading a report
// Asking a few runners about the course
⏱ about 20 min

Friday: Reading a Report

Comet holds up a flyer she made as a test. "9 out of 10 runners love the new course!"

"Who was asked?" Wren says at once. "How were they picked? What exactly was the question?"

"My 10 friends at the finish," Comet admits. "And I asked, 'Isn't the new course great?'"

"Convenience sample, leading question, tiny sample," Wren says. "Three problems in one flyer. What do you notice?"

"The 90% is real arithmetic," Comet says. "But it tells us nothing about all 40 runners."

Nova projects a checklist beside the flyer. "Would you like a hint? Ask the same five questions of every report."

"Population, sample size, how picked, what asked, and what the number means," Wren says. "Every time."

Five questions for any report

  • What population is the report about? Does the sample come from that population?
  • How big was the sample? A small sample wobbles a lot.
  • How was the sample picked? Random, convenience or voluntary?
  • What exactly was asked? Was the wording neutral?
  • What does the number mean? A percent of whom, and compared with what?

Comet's flyer: population unclear, sample of 10, picked by convenience, a leading question, and a percent of friends only.

The crew's Monday survey: population all 40 runners, sample of 10, picked by the bag, a plain question, 60% of the sample.

Even the Monday survey is an estimate with wobble. A careful report says so.

ReportSample sizeHow pickedQuestionTrust it?
Comet's flyer10friends at the finishleadingno
Monday's survey1010 tokens from 40neutralyes, with wobble
A sheet at the water tablewhoever writesvoluntaryneutralno

Review: the week in one list

  • Population and parameter: the whole group and its number. Sample and statistic: the part asked and its number.
  • Random selection makes a sample fair. Random assignment makes an experiment fair.
  • Survey, experiment, observational study: ask where the chance is.
  • Statistics wobble from sample to sample, but random samples center near the parameter.
  • Convenience, voluntary response and leading questions make a report lean. Ask the five questions.
MIXED REVIEW
  • Read the question.
  • Tap your answer.
Comet's flyer says 9 of 10 runners love the course. What percent is that? (Round to 1 place.)
Comet asked 10 friends at the finish, "Isn't the new course great?" What is the main problem, if any?
The flyer's 90% came from the 10 runners Comet asked. Is that number a parameter or a statistic?
The crew assigns runners by a fair draw to the old loop or the new loop, then times them. What kind of study is this?
WHICH CONCLUSION IS JUSTIFIED?
  • Read the question.
  • Tap your answer.
Comet's flyer says 90% love the course. What can the crew conclude about all 40 runners?
Monday's random sample of 10 gave 60% yes. Which sentence is the careful one?
A report compares runners who chose to stretch with runners who did not, and says stretching causes speed. What is wrong?
How many problems did Wren find in Comet's flyer? Type the number.
WHY THIS EXERCISECounting the problems is the start. Naming them is the skill.
StatementTrue or false?
A percent from 10 friends tells you about all 40 runners.?
A careful report says how the sample was picked.?
9 + 1 = 10?
A random sample gives an estimate with some wobble, and a good report says so.?
WHY THIS EXERCISEThe five questions turn a flashy number into something you can judge.
Try it
Find any claim with a percent in it. Ask the five questions and write down which ones it does not answer.
Rewrite the claim in careful words, naming the sample size and how it was picked.
Draw Comet's flyer and, beside it, a corrected version with the sample size and the way it was picked.

A critical reader. Tomorrow is Track Day: a random sample from your own shelf, and an estimate for the family.

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