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Worked-example setupScope and assumptions
- Both selected series use the same ratio-scale variable and whole-calendar-day definition.
- Each row receives equal invoice weight.
- Quartiles use the median-of-halves-exclusive convention and potential outliers remain in every primary summary.
- Period
- Separate fictional 2025 and 2026 invoice samples
- Units
- Whole calendar days; variance in squared days
- Rounding
- Full precision internally; means, medians, and spread displayed to two decimals where noted
Compute center from the complete selected values
Year 1 totals 510 days; Year 2 totals 470. Dividing each by 16 gives means of 31.875 and 29.375 days. The respective middle pairs give medians of 31.5 and 26.5 days.
| Sample | Mean | Median | Mean minus median |
|---|---|---|---|
| Year 1 | 31.875 | 31.5 | 0.375 |
| Year 2 | 29.375 | 26.5 | 2.875 |
Year 2's larger mean-minus-median gap is consistent with its long upper tail. It is not a formal skewness test.
Compute spread under the sample convention
| Sample | Q1 | Q3 | IQR | Range | Sample variance | Sample standard deviation |
|---|---|---|---|---|---|---|
| Year 1 | 27.5 | 35.5 | 8.0 | 22 | 34.25 day² | 5.85235 days |
| Year 2 | 22.5 | 30.5 | 8.0 | 60 | 190.78333 day² | 13.81243 days |
The IQR is identical because both middle halves span eight days. The range and standard deviation differ sharply because they respond to the 78-day tail. This is why “spread” is not one interchangeable number.
Interpret at the sample level
Year 2's selected invoices have lower center by both measures and much greater deviation-based spread. Most Year 2 observations are shorter than most Year 1 observations, while one is far longer. The comparison describes these 32 records.
It does not show that Juniper's full Year 2 population settled faster, that a policy caused a change, or that future cash collection improved. Those claims need population inference, source evidence, and—depending on the claim—a comparison or causal design not supplied here.
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.
- comparisons
- 1 field
Inspect data
{
"year_2_vs_year_1": {
"direction": "right-minus-left",
"left": "year_1",
"right": "year_2"
}
}- series
- 2 fields
Inspect data
{
"year_1": {
"dispersion_convention": "sample-n-minus-one",
"inference_basis": "simple-random-sample",
"mean_confidence_interval": {
"confidence_level": 0.95,
"critical_value": 2.131449545559323,
"degrees_of_freedom": 15,
"interval_scope": "two-sided-one-sample-mean",
"reference_distribution": "student-t-supplied"
},
"missing_value_policy": "reject",
"observations": [
22,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
38,
40,
44
],
"outlier_policy": "retain-and-flag",
"population_role": "sample",
"quartile_method": "median-of-halves-exclusive"
},
"year_2": {
"dispersion_convention": "sample-n-minus-one",
"inference_basis": "simple-random-sample",
"mean_confidence_interval": {
"confidence_level": 0.95,
"critical_value": 2.131449545559323,
"degrees_of_freedom": 15,
"interval_scope": "two-sided-one-sample-mean",
"reference_distribution": "student-t-supplied"
},
"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 |
|---|---|
| 1 first quartile | 27.5 |
| 1 mean | 31.875 |
| 1 median | 31.5 |
| 1 sample standard deviation | 5.8523 |
| 1 sample variance | 34.25 |
| 1 sum | 510 |
| 1 third quartile | 35.5 |
| 2 first quartile | 22.5 |
| 2 mean | 29.375 |
| 2 median | 26.5 |
| 2 sample standard deviation | 13.8124 |
| 2 sample variance | 190.7833 |
| 2 sum | 470 |
| 2 third quartile | 30.5 |
| 2 vs year 1 right minus left mean | -2.5 |
| 2 vs year 1 right minus left median | -5 |