"Two notes on the board," Comet says. "One says 'Most runners want to keep the stretch.' No numbers."
"The other says '65% of 80 sampled cards said keep the stretch, plus or minus 10.7%.' What do you notice?"
"The second one can be checked," Wren says. "Sample size, percent, margin. The first one is just a feeling."
"Even the second has a catch," Comet says. "The interval runs 54.3% to 75.7%. Still above half, so the claim holds."
Nova lifts the first note. "Would you like a hint? Ask who was asked, how many and how."
"If the 80 cards were drawn from the bag, fair," Wren says. "If they were the first 80 in line, that is a convenience sample."
"So a report needs the count, the method and the bracket," Comet says. "Or it is just chalk."
"Then our poster gets all three," Wren says.
A good report based on data says how many were sampled and how they were chosen. It gives the percent or mean found, and the margin.
Missing the sample size: you cannot find the margin. Missing the method: you cannot trust the sample. Missing the margin: the number looks exact when it is not.
A margin can also settle a claim. If the whole interval sits above 50%, "most" is justified. If it crosses 50%, it is not.
| Report | Sample size | Method | Margin | Can it be judged? |
|---|---|---|---|---|
| "Most runners want to keep the stretch." | missing | missing | missing | no |
| "65% of 80 cards drawn from the bag said keep it, ± 10.7%." | 80 | random draw | 10.7% | yes |
| "65% of the first 80 runners in line said keep it." | 80 | convenience | missing | only with care |
| Statement | True or false? |
|---|---|
| 52 ÷ 80 = 0.65 | ? |
| A percent with no sample size can still be given a margin. | ? |
| A convenience sample is a problem even if the sample is large. | ? |
| "Most" is justified when the whole interval sits above 50%. | ? |
A clear-headed week. Tomorrow is Track Day: your family draws from a bag and builds a bracket of their own.