Samples are not all the same length, so their grades cannot simply be averaged. A straight average of unequal samples is the single commonest arithmetic error in exploration — and it flatters short high-grade samples, which is the direction that costs money.
The cut-off grade is not geology. It is the grade at which the metal pays for getting it out, and it moves with the price, the cost and the recovery — which is why a resource shrinks and grows without anybody drilling anything.
This is the marginal cut-off — it pays for processing a tonne already broken. A tonne that must also be mined and hauled carries those costs too, and the difference between the two cut-offs is what decides whether marginal material is mined or left.
Raise the cut-off and the tonnage falls while the grade rises. The curve those two trace is the most honest single picture of a deposit — and it shows at a glance whether the thing is a few rich blocks or a large mediocre mass.
Volume times density. The density is measured, never assumed — a sulphide body and its host can differ by a third, and using one figure for both moves the tonnage by more than any geological argument in the report.
Resource categories are not adjectives. Under JORC, NI 43-101 and the other CRIRSCO codes they are defined terms with legal weight, and a competent person signs their name against them. The distinction is entirely about confidence, and confidence comes from spacing, from continuity, and from whether the assays can be trusted at all.
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Inferred material may not be used in a reserve, and a resource is not a reserve until modifying factors — mining, processing, permitting, economics — have been applied and it still pays. Reporting a resource as though it were a reserve is the failure mode that ends careers.
The intersection length that goes into a composite must be a true thickness, not a down-hole length, and the assays behind it must have survived QA/QC. Both come before any of this arithmetic means anything.