cs-098 — Screen Time by Cohort
| Field | Value |
|---|---|
| id | cs-098 |
| difficulty | Foundational |
| topics | data, distributions |
| lecture | lecture-25 |
| estimated time | 5-minute attempt + 10-minute discussion |
| prerequisites | lectures 1-2 (problem framing, precise pseudocode) |
| objective | recognise the pattern, translate it into precise steps, and trace it correctly |
| solution | held by the instructor; discussed after the attempt |
Problem
Compare app usage across three student cohorts with counts, shares, and a distribution sketch. Choosing summaries that answer the actual question.
Your deliverable is the stated assumptions, the cohort averages computed correctly, and one split (by hour, by cohort) that reverses the naive conclusion. If the problem is ambiguous anywhere, state the assumption you are making and carry on — a stated assumption is part of a good answer.
Examples
- Input: cohort A app minutes [120, 90, 150]; cohort B [60, 45, 75]; cohort C [200, 180, 210, 190]
- Output: A mean 120, B mean 60, C mean 195; shares of total usage differ from headcount shares
Solve for the worked instance first. Then ask what would change if one number, name, or condition were replaced by something stranger.
What to notice
- Compute mean AND share of total; the two rankings can disagree - that disagreement is the finding.
- Writing the rules IS the solution; code is transcription.
- Every assumption is a place where two good answers can differ.
Discussion starter
After the solution is revealed, the class spends five minutes on this prompt: "Which assumption would you attack first if you had to argue the other side?"
Constraints and assumptions
- Difficulty: Foundational (early-semester techniques assumed: precise statements, traces, simple loops).
- Topics: data, distributions.
- Classroom-scale inputs unless the problem says otherwise.
- Time-box: about five minutes; naming the pattern and stating the assumption is already a pass, completing the calculation is the stretch.
- Optional stretch (not required): describe an alternative approach and say when it beats the obvious one.
Hints and extension
- First nudge: identify the pattern the worked instance uses before computing anything.
- If stuck after three minutes, write the input/output line you expect and trace the smallest example by hand.
- After the reveal, attempt the extension below before the next lecture.
- Extension challenge: Find the aggregation that answers a different stakeholder's question.