Understand distributions instead of relying on one average
Learn the reasoning. Try the task. Compare your answer.
Prepared for DataCareerHub · Curriculum version 2026-10-15.2
By the end of this lesson
- Calculate response durations with consistent units.
- Compare mean, median, range and the underlying observations.
- Explain why an extreme valid value is not automatically an error.
Harbor Helpdesk · UTC · Snapshot 22 June 2026 00:00 · Prepared fictional extract · No Python or SQL required.
Understand the method
An average compresses many observations into one number. That can be useful, but it can also hide a slow tail, separate subgroups or a change in composition. Inspect the response-duration distribution before describing a “typical” experience. State exactly what is being averaged and keep time units consistent across every calculation and chart.
Derive elapsed hours
For each observed response, subtract ticket creation from the first human-response timestamp and divide elapsed seconds by 3,600. If a spreadsheet stores valid timestamps as serial days, multiply the day difference by 24. Verify that import converted ISO text to timestamps first and kept UTC consistent; blindly multiplying text or workstation-local times is not a valid calculation. Do not subtract only the clock hour: crossing midnight still adds elapsed hours.
Keep ticket IDs beside derived durations so an unusual value can be traced to its source. The prepared file has no negative or unobserved response durations. Its response times range from 0.25 hours to 8 hours. Those are 15 minutes and 480 minutes respectively. A value of 0.25 hours is not 25 minutes, and 3.3125 hours is not three hours and 31 minutes. Convert the fractional hour by multiplying it by 60 when writing a clock-style explanation.
Calculate and compare summaries
Week 1's 12 response durations sum to 39.75 hours. The mean is 39.75/12 = 3.3125 hours, or 198.75 minutes. When sorted, the sixth and seventh values are 2 and 3 hours; their midpoint gives a median of 2.5 hours. Week 2 sums to 33 hours, with mean 2.75 hours and median 2 hours. Both cohorts have the same minimum of 0.25 hours and maximum of 8 hours. A lower mean does not imply every ticket became faster or the slowest wait improved.
The combined mean is 72.75/24 = 3.03125 hours and the combined median is 2 hours. Pooling can be appropriate for a description of all supplied tickets, but it removes the comparison the manager asked about. Avoid mixing a pooled statistic with a weekly conclusion. In this specific file equal cohort sizes make the unweighted average of the two weekly means equal the pooled mean; that shortcut fails when denominators differ.
Do not erase inconvenient observations
The median is less affected by the largest values than the mean, but it is not automatically the “correct” measure. A service team may care about both the common experience and the slowest waits. Inspect the sorted values or a distribution plot, then use a summary that answers the question. An eight-hour response is a valid recorded observation in this case. No operational threshold supplied here makes it a source error or authorizes its exclusion.
If you explore an exclusion scenario, label it separately, explain the rule and retain the full-data baseline. Do not replace the original mean with a more attractive figure after removing slow tickets. The business target is four-hour timeliness, a proportion, so duration summaries complement that measure rather than replacing it. Finish with a precise statement: recorded mean and median are lower in the second cohort, while the observed maximum is unchanged; the reason for these differences is not established by these summaries.
Practical exercise
Derive or inspect all response durations, retaining ticket IDs. Calculate sum, mean, median, minimum and maximum for each cohort and for the combined extract. Show the two central sorted values used for each even-sized median.
- Convert 0.25 and 3.3125 hours into minutes.
- Explain why a lower mean and an unchanged maximum can both be true.
- Write two sentences comparing the cohorts without claiming every ticket improved.
- State what evidence would be needed before removing an eight-hour record.
Open the worked solution
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.
One more question.
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