This example shows why Minerallum separates measured-point results from interpolated estimates.
Data
| Opening | Mass retained |
|---|---|
| 1000 µm | 5 g |
| 500 µm | 20 g |
| 250 µm | 40 g |
| 125 µm | 25 g |
| Pan | 10 g |
Recovered mass:
M = 5 + 20 + 40 + 25 + 10 = 100 g
Exact distribution
| Opening | Retained | Cumulative retained | Passing |
|---|---|---|---|
| 1000 µm | 5% | 5% | 95% |
| 500 µm | 20% | 25% | 75% |
| 250 µm | 40% | 65% | 35% |
| 125 µm | 25% | 90% | 10% |
| Pan | 10% | 100% | - |
These values do not depend on interpolation.
D10
10% passing occurs exactly at 125 µm:
D10 = 125 µm
Status: measured sieve point.
D50 without interpolation
50% is bracketed by:
- 250 µm at 35% passing;
- 500 µm at 75% passing.
Default result:
D50 ∈ [250, 500] µm
No single value is invented.
D50 using linear-size interpolation
alpha = (50-35)/(75-35) = 0.375
D50 = 250 + 0.375 × (500-250)
D50 = 343.750000 µm
D50 using log-size interpolation
D50 = 250 × (500/250)^0.375
D50 = 324.209889 µm
The same measured points produce different estimates because the between-point model differs.
D90
90% is bracketed by:
- 500 µm at 75%;
- 1000 µm at 95%.
No interpolation:
D90 ∈ [500, 1000] µm
Linear-size:
D90 = 875.000000 µm
Log-size:
D90 = 840.896415 µm
Span
Span is unavailable in bracket-only mode because D50 and D90 are intervals rather than scalars.
Linear-size:
Span = 2.181818
Log-size:
Span = 2.208126
The method belongs with the result.
Pan
The 10 g pan fraction contributes to recovered mass but is never treated as a 0 µm opening.
Key point
The cumulative table follows directly from the entered masses.
Interpolated values are not new measurements. They are estimates between measured points under an explicitly selected method.