Explore first. Explain carefully.
This is a complete guided educational example on a deliberately constructed 24-ticket extract, not real client work, a causal evaluation or a representative business sample. Attempt the worksheet before reading the solution. No controls refresh this static page from a neighbouring CSV.
Unchanged ticket source · Source dictionary · Checked results and durations · Optional read-only Python · Exercises · Rubric
One source, explicit boundaries.
One row per fictional ticket, 24 unique keys; source is byte-identical to Applied Module 01. Creation cohorts: [1 June 2026 00:00, 8 June 00:00) and [8 June 00:00, 15 June 00:00), UTC. Snapshot: 22 June 00:00 UTC. Each cohort has 12 tickets, 12 observed responses and sufficient 72-hour follow-up. Six first resolutions and eight ratings are blank under the documented dictionary; retain their tickets.
A mean needs its surrounding evidence.
| Elapsed hours | Week 1 | Week 2 | Combined |
|---|---|---|---|
| Observed | 12 | 12 | 24 |
| Sum | 39.75 | 33 | 72.75 |
| Mean | 3.3125 | 2.75 | 3.03125 |
| Median | 2.5 | 2 | 2 |
| Minimum / maximum | 0.25 / 8 | 0.25 / 8 | 0.25 / 8 |
Mean and median are lower in Week 2, but each cohort still has an eight-hour response. Do not delete valid slow records or claim every ticket improved.
Same categories. Visible counts.
These are count bars across unequal-width interval categories, not a density histogram. Each cohort sums to 12. Labels and numbers carry the meaning independently of colour.
Week 1
- [0,1) hours · 2 tickets
- [1,2) hours · 2 tickets
- [2,4) hours · 3 tickets
- [4,8) hours · 4 tickets
- [8,infinity) hours · 1 ticket
Week 2
- [0,1) hours · 3 tickets
- [1,2) hours · 2 tickets
- [2,4) hours · 3 tickets
- [4,8) hours · 3 tickets
- [8,infinity) hours · 1 ticket
Exactly 4h belongs in [4,8) but is timely under the inclusive ≤4h policy. Add the exactly-4h counts (1 and 2) to the first three bin totals (7 and 8) to recover 8 and 10 timely tickets. Exactly 8h belongs in [8,infinity).
Changed mix, unchanged channel rates.
| Group | W1 timely / tickets | W2 timely / tickets | W1 ratings / tickets | W2 ratings / tickets |
|---|---|---|---|---|
| 4/8 · 50% | 2/4 · 50% | 8/8 | 4/4 | |
| Chat | 4/4 · 100% | 8/8 · 100% | 0/4 | 4/8 |
| Total | 8/12 · 66.67% | 10/12 · 83.33% | 8/12 | 8/12 |
Observed timeliness rises by 16.67 percentage points (25% relative rate change). Under fixed Week 1 weights (2/3 email, 1/3 chat), both rates are 66.67%. Under equal channel weights both are 75%. These standardized descriptions are neither the observed ticket rates nor causal effects.
Respondent rating means are 4.0/5 where ratings exist. Week 1 chat mean is unavailable, not zero or 4.0, because no rating is observed. Equal weekly respondent means do not establish equal satisfaction for all tickets.
The 72-hour first-resolution guardrail is 9/12 (75%) in both cohorts. High-priority timeliness is 2/3 then 3/3: one ticket changes a three-ticket rate by 33.33 percentage points. Show counts; do not turn tiny exploratory cells into operational certainty.
Profile the extract before looking for patterns
Profile: 24 records, 24 unique nonblank keys, 12 tickets per creation cohort, email/chat categories, general/billing queues and high/normal priorities. First responses observed: 24/24. Missing first resolutions: six, three per cohort. Missing ratings: eight, four per cohort. Every record is mature for 72 hours at the stated cutoff.
Checks: key uniqueness → investigate conflicts; parseable UTC dates → quarantine malformed rows; creation in cohort interval → count exclusions; events after creation and no later than cutoff → investigate chronology; categories/ratings within dictionary → flag unsupported values; counts by cohort and maturity → reconcile before rates. Prepared source passes these conditions. Missing ratings remain outside the rating mean only; mature non-resolutions stay in the guardrail denominator. None of this establishes that the fictional file covers the whole organization's activity or identifies routing exposure.
Understand distributions instead of relying on one average
Week 1: sum 39.75h, n=12, mean 3.3125h, middle values 2h/3h, median 2.5h, range 0.25–8h. Week 2: sum 33h, n=12, mean 2.75h, middle values 2h/2h, median 2h, same range. Combined: sum 72.75h, n=24, mean 3.03125h, middle values 2h/2h, median 2h, range 0.25–8h.
0.25h = 15 minutes; 3.3125h = 198.75 minutes. A mean uses all observations; changing the mass of shorter/longer waits can reduce it while the largest recorded wait remains eight hours. Suggested statement: “The supplied second cohort has a lower recorded mean and median response duration. Both cohorts still contain an eight-hour response, and these summaries do not establish a routing effect or improvement for every ticket.” Removal needs an authoritative source correction or a justified separately labelled scenario; extremeness alone is insufficient.
For a cross-midnight check, HH002 starts at 21:00 UTC on 1 June and receives its response at 00:00 UTC on 2 June: three elapsed hours. Subtracting only clock-hour numbers would incorrectly produce a negative value. The median is the midpoint of the two central sorted observations, not the midpoint of the range.
Choose charts that reveal rather than manufacture patterns
Bin counts are W1 [2,2,3,4,1], W2 [3,2,3,3,1]. Exactly 4h belongs in [4,8), exactly 8h in [8,infinity). The first three bins total 7 and 8, not the timely 8 and 10: add the exactly-4h counts of 1 and 2 for the inclusive service measure.
Suggested views: cohort dot plots on the same elapsed-hour scale with a labelled 4h reference; a zero-based count/rate comparison with n=12 per cohort; a channel-composition count table or 100% bar with both labels and fractions. Title: “Recorded timeliness rises while channel composition changes.” Describe dates, snapshot and the absence of causal attribution. If rendering bins as equal-width categories, label them as frequency categories; do not imply equal numeric intervals. Provide a table and text summary so meaning survives monochrome display and screen-reader use.
For a rate chart, retain the denominators rather than substituting bins: the visual must still communicate 8/12 and 10/12. With an open-ended final category there is no finite bin width to use for an ordinary density height; a labelled count-category display avoids that unsupported conversion.
Compare groups and separate composition from performance
W1: email 4/8=50%, share 2/3; chat 4/4=100%, share 1/3; total 8/12=66.67%. W2: email 2/4=50%, share 1/3; chat 8/8=100%, share 2/3; total 10/12=83.33%. The unweighted 75% gives both channels equal importance despite their unequal ticket counts.
With W1 weights, both standardized rates are 66.67%; with W2 weights, both are 83.33%. Label the chosen reference and retain observed results. “Observed timeliness rises by 16.67 percentage points in this extract. Under a fixed W1 channel composition, the channel-rate summary is unchanged.” This is descriptive decomposition, not an intervention effect estimate. High-priority timeliness is 2/3 then 3/3; a single observation changes that group's rate by 1/3, or 33.33 percentage points. Exposure needs an authoritative deployment/assignment record; classifications do not provide it.
The change in chat share is 1/3 and the gap between channel rates is 1/2. Their product is 1/6, matching the observed 16.67 percentage-point rise. This algebra reconciles the simple constructed example; it does not explain why channel choice changed or what each ticket would have experienced under a different routing process.
Investigate missingness and alternative explanations
W1 email: 8/8 ratings, mean 4.0; chat: 0/4, mean unavailable. W2 email: 4/4, mean 4.0; chat: 4/8, mean 4.0. Overall per week: 8/12 observed, mean 4.0 among respondents. Across both cohorts, email has 12/12 coverage and chat 4/12. The unobserved opinions remain unknown, so equal respondent means do not establish equal satisfaction for all tickets or customers.
Deleting unrated tickets would discard valid response observations and alter channel composition. Explanation ledger examples: changed chat share → entry-page visibility may affect channel choice → request entry/exposure logs; uneven rating coverage → survey delivery may differ → request survey-offer/delivery events; lower mean duration → mix or staffing may matter → request roster/exposure and longer event history. These are questions, not discovered causes. Missing training arrivals on the last day of each window do not prove zero operational demand; two cohort summaries cannot establish a seasonal pattern.
Turn explored patterns into an evidence note
Worked note: In the supplied 24-ticket Harbor Helpdesk teaching extract, recorded four-hour response timeliness rises from 8/12 (66.67%) in the 1–7 June creation cohort to 10/12 (83.33%) in 8–14 June: a 16.67 percentage-point difference. All tickets have recorded responses and adequate follow-up at the 22 June cutoff. Email timeliness remains 50% and chat 100%, while chat's ticket share rises from 4/12 to 8/12. A fixed Week 1 channel-weight comparison is unchanged at 66.67%, so the headline needs composition context. The 72-hour first-resolution guardrail stays at 9/12 (75%). Mean and median response duration are lower, but both cohorts still include an eight-hour response. Respondent satisfaction means are 4.0/5 with only 8/12 ratings per cohort and uneven channel coverage. Concurrent staffing/entry changes, absent routing exposure and the deliberately small constructed source prevent causal or business-wide conclusions. I propose verifying exposure and survey definitions with the data owner, requesting staffing and a longer consistent event history, and agreeing evaluation criteria before a rollout decision.
Extension: 0.5×50% + 0.5×100% = 75% in both cohorts. These are equally weighted channel summaries, not the observed ticket rates or a causal intervention effect. Observation: chat share rises. Hypothesis: entry visibility changed channel choice. Unsupported claim: routing caused an improvement. Your own note may prioritize different descriptive details if all definitions and limits remain correct.