Key takeaways
- Name the statistic and the time boundary before describing performance.
- Examine whether a few long observations drive the average.
- Keep changes in the typical observation separate from changes in the tail.
- Avoid turning a small historical sample into a forecast for the nominated vessel.
The example below is an original fictional dataset. It contains no actual port performance, current waiting times or statistical claim about a real location. Its purpose is to demonstrate how an accurate calculation can support an inaccurate headline.
State what the number summarises
A reported duration needs both an event definition and a statistical definition. The reader should know whether it concerns waiting before a service, time at berth or another call boundary, and whether the figure is a mean, median or another measure.
The mean adds the observations and divides by their number. The median identifies the middle of the ordered observations, averaging the middle pair for an even-sized sample. These measures can respond differently to the same dataset.
Neither is automatically the right measure for every commercial question. A desk interested in total time across a sample may need one perspective, while a desk examining the typical observation may need another. A concern about unusually long outcomes may require looking beyond both.
The report should state the question before selecting the headline statistic. Choosing the most favourable number after inspecting the data can obscure the pattern the reader needs to understand.
Illustrative correction: the mean falls while the median rises
ILLUSTRATIVE — invented waiting durations in days, with the same defined event boundary. The first sample contains 6 observations: 1, 1, 1, 1, 1 and 13. The second sample contains 6 observations: 2, 2, 2, 2, 2 and 2.
| Fictional summary | First sample | Second sample | Change |
|---|---|---|---|
| Number of observations | 6 | 6 | Unchanged |
| Total waiting days | 18 | 12 | −6 days |
| Mean waiting time | 3 days | 2 days | −33.33% |
| Median waiting time | 1 day | 2 days | +100% |
| Longest observation | 13 days | 2 days | −11 days |
The flawed headline is: “Waiting falls by a third, so calls are faster.” The mean did fall by 33.33%, but the statement generalises that result to all calls. The first sample has 5 observations at 1 day, whereas every observation in the second sample is 2 days.
A corrected headline is: “Mean waiting falls as the long observation disappears; median waiting rises.” The report can then explain that total waiting is lower across the second sample while its middle observation is longer.
The samples are invented and not paired observations of the same vessels. The comparison therefore does not claim that a particular ship's wait changed from 1 to 2 days or that the next call will wait 2 days.
Explain the mechanism rather than choosing a winner
The example does not show that the mean is wrong or the median is always better. Each describes a different feature of the observations. The reporting error is the unsupported interpretation attached to the mean.
A large change in an extreme observation can materially affect the mean. That may be commercially important, especially where the concern includes aggregate time or unusually long cases. At the same time, it can conceal a different movement in the middle of the sample.
Present the relevant views together where they answer different parts of the decision. The reader should not have to choose between an optimistic and pessimistic statistic without understanding what each measures.
Avoid describing the disappearance of a long observation as proof that the underlying cause has been resolved. The sample alone shows the observation pattern. An explanation of cause requires additional evidence.
Check whether the samples are comparable
Before interpreting any statistical change, confirm that the event boundary, vessel group, service scope and period are sufficiently comparable. A different call mix can alter the distribution without establishing a performance change for like-for-like work.
The dataset should also distinguish complete and incomplete observations. If a current wait is still ongoing, its eventual duration is not yet known. Treating the elapsed time as a completed wait can distort the comparison unless the method explicitly addresses that status.
Do not silently remove long observations because they make the report inconvenient. Investigate whether they are valid, relevant or erroneous under the stated rules. Any exclusion should follow a defensible method and be explained where material.
The same discipline applies to missing records. A cleaner-looking dataset is not necessarily a more representative one if difficult cases have simply disappeared from the sample.
Keep the nominated call outside the historical average
A historical summary can frame the commercial discussion, but it does not determine the next vessel's waiting time. The nominated call has its own service, readiness and timing conditions.
Use the sample to identify questions or build clearly labelled planning scenarios. Do not present the central measure as a berth estimate unless the relevant current evidence supports that use.
The commercial team may care more about a particular deadline than the average experience. In that case, examine the relevant uncertainty and programme consequence rather than assuming the average answers the deadline question.
A small fictional or historical sample also does not justify precise probabilities. Preserve the limits of the evidence and seek the appropriate call-specific information.
Repair the recommendation that used the headline
If the original report supported an alternative-port or timing decision, revisit that recommendation after correcting the interpretation. A lower mean may still be relevant, but the decision may also depend on variation, current-call conditions and complete costs.
State what changed in the analysis. The correction may concern the headline's generalisation rather than the arithmetic. Readers should understand that the original mean can remain valid while the claim that every call is faster is withdrawn.
Do not overcorrect by ignoring the improvement in the long-duration observation. Preserve the evidence on both sides and relate it to the actual commercial question. The objective is an accurate account, not a reversal of tone for its own sake.
Use a distribution-aware reporting checklist
- Name the time event, unit and summary statistic.
- Verify comparable sample scope and observation status.
- Inspect the distribution and the influence of long observations.
- Explain whether the central tendency and extreme outcomes move differently.
- Separate observed patterns from causal explanations and future-call forecasts.
- Reassess commercial conclusions that relied on a broader claim.
The checklist should be applied before the headline is shortened for circulation. A concise message can retain the statistic's name and scope without reproducing every data point.
Preserve a clear analytical boundary
The final report should say what the sample shows, what remains uncertain and why the distinction matters to the decision. It should not turn a descriptive statistic into a universal judgement about a port or terminal.
Where the available data cannot answer the commercial question, state the missing evidence. A transparent limitation is more useful than a precise figure carrying an unsupported interpretation.
Retain the calculation and any exclusion rules with the report. That allows the next reviewer to update the analysis consistently rather than inheriting only the earlier headline.
Common mistakes
Calling a mean reduction improvement for every call. Inspect the distribution before generalising.
Treating the median as universally superior. Choose measures that answer the actual question and explain their differences.
Removing long observations without a stated rule. Verify relevance and data quality rather than selecting a convenient sample.
Using historical averages as call commitments. Obtain current evidence for the nominated vessel's programme.
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Educational information only; not legal, financial or trading advice. Contract wording and applicable rules control. Verify current requirements and obtain qualified advice before acting.
Frequently asked questions
Can mean waiting fall while median waiting rises?
Yes. The invented dataset demonstrates that pattern when a long observation changes the mean while the middle of the sample moves differently.
Which statistic should the report use?
Use the measure appropriate to the question, and show additional distribution information where material. No single statistic answers every commercial concern.
Should unusually long observations be removed?
Only under a defensible relevance or data-quality method. Their inconvenience is not a reason for exclusion.
Does the corrected sample predict the next call?
No. It describes the selected observations. The nominated call needs relevant current information and an explicit planning assessment.
What makes the correction complete?
Preserve valid arithmetic, correct the interpretation and revisit any recommendation that relied on the broader claim. Explain the remaining uncertainty clearly.