Worked-example setupScope and assumptions
- The eight values are a complete fictional teaching population.
- The four size-four subsets illustrate possible samples; their display frequency is not a probability model.
- Each observation receives equal weight.
- Period
- One fictional fixed population period
- Units
- Whole calendar days
- Rounding
- Means exact; variance and standard deviation retain full precision
Fix the target
The complete population is [10, 20, 30, 40, 50, 60, 70, 80] days. Its mean
parameter is 45 days. Because all eight values are visible, the population
variance uses (N=8) and equals 525 day².
Select different subsets
| Possible size-four sample | Sample mean |
|---|---|
| A: 10, 20, 30, 40 | 25 days |
| B: 50, 60, 70, 80 | 65 days |
| C: 10, 30, 50, 70 | 40 days |
| D: 20, 40, 60, 80 | 50 days |
The population and parameter did not change. The selected units did, so the statistics changed. That is sampling variability.
These four displayed subsets are not a complete randomization distribution, and their frequency is not used to estimate a standard error. They make the object distinction visible before probability is introduced.
Transfer to Juniper
Juniper observes one sample per year, not repeated samples from one visible population. Its means may differ because the selected units differ and because the year-specific populations may differ. A year label does not identify the mixture. The interval method models one component of uncertainty under stated conditions; source and business-change evidence remain separate.
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
- 5 fields
Inspect data
{
"all_invoices": {
"dispersion_convention": "population-n",
"inference_basis": "complete-population",
"mean_confidence_interval": null,
"missing_value_policy": "reject",
"observations": [
10,
20,
30,
40,
50,
60,
70,
80
],
"outlier_policy": "retain-and-flag",
"population_role": "complete-population",
"quartile_method": "median-of-halves-exclusive"
},
"sample_a": {
"dispersion_convention": "sample-n-minus-one",
"inference_basis": "descriptive-only",
"mean_confidence_interval": null,
"missing_value_policy": "reject",
"observations": [
10,
20,
30,
40
],
"outlier_policy": "retain-and-flag",
"population_role": "sample",
"quartile_method": "median-of-halves-exclusive"
},
"sample_b": {
"dispersion_convention": "sample-n-minus-one",
"inference_basis": "descriptive-only",
"mean_confidence_interval": null,
"missing_value_policy": "reject",
"observations": [
50,
60,
70,
80
],
"outlier_policy": "retain-and-flag",
"population_role": "sample",
"quartile_method": "median-of-halves-exclusive"
},
"sample_c": {
"dispersion_convention": "sample-n-minus-one",
"inference_basis": "descriptive-only",
"mean_confidence_interval": null,
"missing_value_policy": "reject",
"observations": [
10,
30,
50,
70
],
"outlier_policy": "retain-and-flag",
"population_role": "sample",
"quartile_method": "median-of-halves-exclusive"
},
"sample_d": {
"dispersion_convention": "sample-n-minus-one",
"inference_basis": "descriptive-only",
"mean_confidence_interval": null,
"missing_value_policy": "reject",
"observations": [
20,
40,
60,
80
],
"outlier_policy": "retain-and-flag",
"population_role": "sample",
"quartile_method": "median-of-halves-exclusive"
}
}Recomputed result
| Measure | Value |
|---|---|
| all invoices mean | 45 |
| all invoices population variance | 525 |
| sample a mean | 25 |
| sample b mean | 65 |
| sample c mean | 40 |
| sample d mean | 50 |