Monday
Monday: Ask a Few, Learn About All
"40 runners signed up," Comet says at the park gate, fanning the cards. "Should we hold a group warm-up?"
"Asking all 40 would take the whole morning," Wren says. "Ask 10. Let the bag pick them."
He drops 40 numbered tokens into the cloth bag and draws 10. Comet finds each card and asks the runner.
"6 yes, 4 no," she reports. "60% want a warm-up. What do you notice?"
"That 60% is about our 10," Wren says. "The number we care about is the percent of all 40."
Nova glows a field of 40 dots with 10 lit. "Would you like a hint? The lit dots speak for the rest."
"A sample speaking for a population," Comet says. "As long as the bag did the choosing, not us."
Population and sample
The population is the whole group the question is about: all 40 runners who signed up.
The sample is the part the crew actually asked: the 10 runners whose tokens came out of the bag.
A number about the whole population is a parameter. The crew does not know it; it would have to ask everyone.
A number from the sample is a statistic. 60% said yes. The statistic is the crew's estimate of the parameter.
Statistics is this process: draw a fair sample, compute a statistic, and use it to infer the population's parameter.
| Word | In the crew's survey | Known? |
|---|---|---|
| population | all 40 runners who signed up | yes, the list of cards |
| sample | the 10 runners the bag picked | yes |
| parameter | the percent of all 40 who want a warm-up | not yet |
| statistic | 6 of 10, which is 60% | yes, from the sample |
A solved problem to study
Here is how Wren turns the sample into an estimate, and later checks it.
- Name the population: all 40 runners. Name the parameter: the percent who want a group warm-up.
- Draw a random sample: 10 tokens from a bag of 40. Chance picks, so every runner has the same chance.
- Compute the statistic: 6 yes out of 10. 6 ÷ 10 × 100 = 60%.
- Infer: about 60% of all 40 probably want a warm-up, give or take, because 10 is a small sample.
- Later the crew asked everyone: 22 of 40 said yes, which is 55%. The parameter was close to the statistic.
Every count here is the crew's own made-up tally from Nova's Run Log, not a real survey of anyone.
- Read the question.
- Tap your answer.
| Statement | True or false? |
|---|---|
| A parameter is a number about the whole population. | ? |
| A statistic is a number from the sample. | ? |
| 6 + 4 = 10 | ? |
| The crew knew the parameter before asking anyone. | ? |
Those are your sample. Write down which numbers came out. Tomorrow you will see why chance did the picking.
A sample that speaks for a group. Tomorrow three kinds of study, and what randomization does in each.