SCIENCE · INVESTIGATE AND EXPLAIN

Inspect who entered the sample

Connect selection rules to a sample's representativeness.

Learning outcome: Compare a sample mean with a known finite population and explain selection bias.

Starting recap

A sample is a subset; a census includes the whole finite population.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

A waiting-time file is sorted from shortest to longest. Reading its first rows favors short waits.

Open the experiment

Predict

Will the first three rows represent the average wait?

Your prediction and reason

Experiment

Compare prefix and spread samples of size 3. Then inspect all ten records.

Inspect a biased sample

Worked teaching model · synthetic values · The finite population is 2, 4, …, 20 minutes, ordered by waiting time. Spread selection is deterministic, not a probability sample or a confidence procedure.

Sample size: 3 records Selection method: 0 first records, 1 spread records: 0

Reset keeps your prediction, captures and practice history.

Calculated values on the same fixed scale
Row	Quantity	Value (minutes)
1	Sample 1	2
2	Sample 2	4
3	Sample 3	6
4	Sample mean	4
5	Population mean	11

Sample mean: 4.00 minutes. Population mean: 11 minutes.

Inspect the selected values. A larger prefix still favors short waits until it becomes a census. A deterministic spread can approximate the mean here but does not justify a probability-based uncertainty interval.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Inspect the selection mechanism before trusting the mean

The complete teaching population contains waits of 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 minutes. Their sum is 110 minutes, so the population mean is 11 minutes.

The first three entries average (2 + 4 + 6) / 3 = 4 minutes. The file’s ordering matters: a prefix preferentially includes short waits. Increasing the prefix to five entries gives a mean of 6 minutes, still below 11.

A census of all ten records recovers this finite population mean. It says nothing about tomorrow’s customers or a different service.

A representative-looking result is not a sampling guarantee

The spread method chooses evenly distributed indices in the ordered list. With three records, it selects 2, 12 and 20 minutes, whose mean is about 11.33 minutes. This is closer here, but the method is deterministic.

A probability sample requires a specified random selection mechanism and appropriate inclusion probabilities. This activity does not supply that mechanism or a confidence interval.

Compare the actual selected rows, not only their average. An empty sample has no defined mean; the controls therefore start at one record. Explain which population your conclusion addresses and which groups could still be missing from a real data source.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Explain why the spread sample's success in this list does not make it a random sample.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Choose controls and independent repetitions Next: Separate random variation from systematic error

Save a science backup or import one

Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.

A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.

Choose a science backup (maximum 36 MB)

Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.

Complete file sets and course backups

A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.

Export scope

The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.

Choose the manifest and all parts together

0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.

Science storage: loading. No account or remote computation is required.