Case Studies · Data Science

Eight supplementary case studies for BS Data Science sections, in the same 5-minute think → discuss → reveal format as the main bank (by_tier/). Numbering uses the PF-DS-CS prefix so the main bank's PF-CS-001…108 stays contiguous. Worked discussion guides live in the instructor area only (../instructor/case_studies/ds_solutions.md).

PF-DS-CS-1 · The Billion-Row Mean

• Tier: 2 Foundational · Lecture: L17 · Module 9
• Context: A teammate computed a dataset's mean, then the data grew 100×.
• Problem: The sum was stored in int. At what dataset size (roughly, values ~1000) does the sum overflow a 32-bit int? What type changes fix it, and which statistic becomes impossible to compute in one pass regardless of types?
• Input/Output: no code required — a numeric estimate + a one-paragraph policy.
• Constraints: only types taught in Modules 2–8.
• Thinking questions: what is int's range? what is the honest failure mode — crash, wrap, or silent wrong answer? what would you print if asked "how big is too big?"
• Expected concepts: integer limits, long long, silent overflow, streaming vs stored data.
• Hints: int tops out near 2.1 × 10⁹ · think total, not mean · what happens to the mean if the sum wraps?

PF-DS-CS-2 · One Missing Sensor Beat the Mean

• Tier: 3 Intermediate · Lecture: L17 · Module 9
• Context: A weather report said "mean temperature 21.0 °C" but one faulty sensor had logged −999 °C for a day.
• Problem: Design the validation rule that would have caught it, the two statistics you can still report honestly with the bad value excluded, and what you must disclose to the report's readers.
• Input/Output: rule in pseudocode; disclosure as a fixed-format footer line.
• Constraints: data in a plain array; values plausible in −50..60.
• Thinking questions: is −999 more like "missing" or "wrong"? why is the median less embarrassed than the mean here? what number belongs next to "n ="?
• Expected concepts: range validation, skip-and-count, robust vs non-robust statistics, honest reporting.
• Hints: −999 was chosen as a sentinel by whoever wrote the logger · mean is a sum divided by what exactly? · disclosure = counts of what you excluded.

PF-DS-CS-3 · The Two-Median Trick

• Tier: 3 Intermediate · Lecture: L17 · Module 9
• Context: A dataset of 7 values grew by 2 new values; someone claims the median is "the average of the two new values."
• Problem: Construct a 7-value dataset and 2 added values where that claim is true, then one where it is badly false. State the correct even-n median rule in your own words.
• Input/Output: two concrete datasets + the rule.
• Constraints: 9 values total; small enough to sort by hand.
• Thinking questions: what must the two new values do to land at the middle? what does the median actually measure — new data, or middle position?
• Expected concepts: median as an order statistic, sorting before medians, why n matters.
• Hints: make the old 7 all tiny · the middle of 9 sorted values is the 5th · "average of two values" needs which two?

PF-DS-CS-4 · The Frequency Table That Lied

• Tier: 3 Intermediate · Lecture: L18 · Module 9
• Context: Ratings run 1..5. A student's table printed six rows — ratings 0..5 — and row 0 said "12 responses."
• Problem: Diagnose the indexing defect (which slot did rating 5 really go to?), state the two standard fixes (shift vs spare slot), and their trade-off for readability.
• Input/Output: defect diagnosis + corrected table sketch.
• Constraints: int counts[6] is the array; no vectors.
• Thinking questions: where did rating 5's vote land? why didn't the program crash? what would happen with rating 6?
• Expected concepts: off-by-one/index shifting, silent corruption vs out-of-bounds, defensive range checks before indexing.
• Hints: C++ indices start at 0 · counts[r] with r = 5 is the sixth slot · validate first, index second.

PF-DS-CS-5 · Skip, Repair, or Abort?

• Tier: 4 Advanced · Lectures: L29–L30 · Module 15
• Context: A grading pipeline reads 5,000 rows; 30 have a missing score, 3 have scores above 100, 1 row is a duplicated header.
• Problem: For each of the three defect classes, choose skip / repair / abort and defend it in one sentence each. Then state the one summary line your pipeline must always print so consumers can judge the data.
• Input/Output: a 3-row decision table + the footer line format.
• Constraints: beginner C++ (streams + arrays); no libraries.
• Thinking questions: which defects are per-row and which poison the whole file? what does a repair need before it is honest? why is exit code 0 correct even when rows were skipped?
• Expected concepts: validation policies, skip-and-report, the audit footer, exit-code discipline.
• Hints: missing ≠ invalid ≠ structural · repaired values must be counted separately · the footer carries the denominators.

PF-DS-CS-6 · Percentile by Hand

• Tier: 4 Advanced · Lecture: L24 · Module 12
• Context: A 12-value sorted dataset; a report asks for "the 75th percentile."
• Problem: Two textbook definitions exist (nearest-rank vs interpolation). Compute BOTH by hand for a dataset of your choosing, explain why they differ, and argue which to ship when the consumer is a school registrar.
• Input/Output: your 12 values + both percentile results + one-sentence justification.
• Constraints: sorted array arithmetic only; no code required.
• Thinking questions: which definition never invents a value that was not in the data? when does the difference vanish?
• Expected concepts: order statistics, definition-dependence of derived numbers, documentation as part of the answer.
• Hints: nearest-rank picks a real data point · interpolation may create a .5 that never existed · consistency across reports beats cleverness.

PF-DS-CS-7 · The Simulation That Looked Rigged

• Tier: 4 Advanced · Lecture: L18 · Module 9
• Context: A student seeded their die simulator with the current time; their classmate's "unusual" results (four 6s in ten rolls) were dismissed as a bug.
• Problem: Is 4 sixes in 10 rolls suspicious for a fair die? Design the counting experiment that answers this over many 10-roll batches, and state what role the seed plays in reproducibility.
• Input/Output: experiment design + expected proportion of "4+ sixes" batches, roughly.
• Constraints: <random> with a fixed seed only; counting loops.
• Thinking questions: what is the expected count of 6s in 10 rolls? what counts as "unusual" — who decides, and from what? why does a fixed seed make the debate finishable?
• Expected concepts: empirical vs expected frequency, simulation as measurement, reproducibility via seeds.
• Hints: expected sixes per 10 rolls is 10/6 ≈ 1.7 · variance makes small batches wobbly · run 10,000 batches and count.

PF-DS-CS-8 · The Report That Could Not Be Rebuilt

• Tier: 5 Expert introductory · Lecture: L30 · Module 15
• Context: Two students produced different means from the same file. One skipped blank lines and quoted lines as data; the other counted blanks as missing.
• Problem: Specify the line-classification contract (exact classes, exact counters, exact footer) that would make both students print identical reports, and identify which number in the report exposes a classification difference fastest.
• Input/Output: a written contract (6–8 lines) + the "fastest tell" number.
• Constraints: getline-based parsing; the footer from PF-DS-CS-5.
• Thinking questions: why did both means look plausible? which counter catches classification drift — loaded, missing, or invalid? what does the class-identity equation enforce?
• Expected concepts: classification contracts, counters as invariants (loaded + missing + invalid = non-blank lines), reproducible pipelines.
• Hints: both forgot the footer · the identity equation fails loudly when classes drift · contracts are documentation that tests can check.