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Worked-example setupScope and assumptions
- The 78-day record is complete, unique, and within the declared target population in the fictional packet.
- Quartiles use the median-of-halves-exclusive convention.
- The 1.5-IQR fence is a screening rule, not an error or fraud test.
- Period
- Fictional Year 2 sample
- Units
- Whole calendar days
- Rounding
- Quartiles and fences exact for the supplied integer series
Apply the screening convention
The lower half of the 16 ordered values has median 22.5; the upper half has median 30.5. Therefore:
[ IQR=30.5-22.5=8, ]
[ \text{lower fence}=22.5-1.5(8)=10.5, \qquad \text{upper fence}=30.5+1.5(8)=42.5. ]
Seventy-eight exceeds 42.5. Label it a potential outlier under this convention. Do not label it wrong.
Build the evidence trace
The fictional packet stipulates that the invoice ID is unique, both required dates are present, and the record meets the population rule. A real review would retrieve:
- invoice issue and due dates;
- all payment and final-application dates;
- dispute, credit-memo, adjustment, and write-off history;
- customer and contract terms;
- join and duplicate diagnostics; and
- the source-query version and extraction timestamp.
Suppose the source showed a transposed final-application date. Correct the record and preserve the correction trail. Suppose instead it showed a genuine contract dispute resolved after 78 days. Retain the record in the primary target population and explain the tail. A separate “undisputed invoices” view would answer another prespecified question; it must not replace the original silently.
Quantify the consequence without using it as a verdict
The record raises Year 2's mean and standard deviation but does not change the median much. Those effects explain why robust companion summaries may help. They do not justify deletion. The treatment follows source evidence and the population definition, not the direction of the result.
Verified calculation · descriptive estimation analysis
The curriculum loader recomputed this example before it entered the site build. Expand any structured input to inspect the stated facts.
- series
- 1 field
Inspect data
{
"year_2": {
"dispersion_convention": "sample-n-minus-one",
"inference_basis": "simple-random-sample",
"mean_confidence_interval": null,
"missing_value_policy": "reject",
"observations": [
18,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
33,
35,
78
],
"outlier_policy": "retain-and-flag",
"population_role": "sample",
"quartile_method": "median-of-halves-exclusive"
}
}Recomputed result
| Measure | Value |
|---|---|
| first quartile | 22.5 |
| interquartile range | 8 |
| lower inner fence | 10.5 |
| maximum | 78 |
| potential outlier count | 1 |
| third quartile | 30.5 |
| upper inner fence | 42.5 |