cs-139 — The Attendance Frame

Field	Value
id	cs-139
difficulty	Intermediate
topics	bias, evaluation, stakeholders
lecture	lecture-25
estimated time	5-minute attempt + 10-minute discussion
prerequisites	lecture-25 (thinking with data) taken in the same session
objective	separate a measurement artifact from a real change by choosing between two frames
solution	held by the instructor; discussed after the attempt

Problem

The library reports: "Weekday visits fell 20% the week after the deadline-week survey." Two staff proposals:

Staff A: "Students are avoiding the library because of the survey. Announce a rollback."
Staff B: "That week contained a four-day holiday. Compare like-for-like before concluding anything."

The visit counts (the log is complete; the difference is the calendar):

Survey week      Mon 520  Tue 540  Wed 500  Thu 530  Fri 510   total 2600
Following week   Mon   0  Tue   0  Wed   0  Thu 490  Fri 480   total  970

The holiday covered Monday–Wednesday of the second week (closed, not a drop in demand).

Your deliverables:

The two frames: total-week comparison versus open-day comparison. Compute both week figures per open day.
What each frame concludes, in one sentence each.
Your verdict with the reasoning rule you would write into the library's reporting policy.
One residual limitation that no frame fixes.

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: the two weeks' visit counts and the holiday window
Output: totals 2600 vs 970 (−63%) — per open day 520 vs 485 (−6.7%) — verdict + policy rule

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

A percentage has no meaning without its base: total-week and per-open-day use different denominators and can disagree in direction, not just size.
Denominator problems are fixable by better framing; nothing here fixes data you did not collect — hence the residual limitation.
Staff A's story and Staff B's story are both consistent with the raw totals; only the frame choice discriminates between them.

Discussion starter

After the solution is revealed, the class spends five minutes on this prompt: "Draft the one-line caveat that must accompany every weekly visits figure in the library's dashboard, whatever the frame."

Constraints and assumptions

Difficulty: Intermediate (metric design and bias reasoning).
Topics: bias, evaluation, stakeholders.
Closed days contribute zero to totals and are excluded from per-open-day averages — state this as part of your frame.
Classroom-scale inputs unless the problem says otherwise.
Time-box: about five minutes for a first attempt; partial answers with clear reasoning are worth more than silent struggling.
Optional stretch (not required): describe an alternative approach and say when it beats the obvious one.

Hints and extension

First nudge: how many days was the library actually open in each week?
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: construct a two-week pattern where the per-open-day frame also misleads, and name the hidden variable.