Mining & Mineral Economics

Sampling & Reserve Estimation

The length-weighted average grade that combines drill-core samples of unequal length into a single representative grade.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Drill-core or channel samples have different lengths, so a simple arithmetic mean is biased. The correct representative grade is the length-weighted average — each grade weighted by its sample length, summed and divided by the total length. This honours the fact that a long, low-grade interval contributes more metal than a short, high-grade one.

The Core Formula Matrix

Length-weighted average grade:

\overset{g}{ˉ} = \frac{\sum ( g _{i} l _{i} )}{\sum l _{i}}

g_{i}

= grade of sample

i

l_{i}

= its length.

The ‘IIT Traps’

⚠
Weight by length, not count. A plain average over-weights short samples.
⚠
Use the metal-content sum $\sum g_{i} l_{i}$ on top, total length on the bottom.
⚠
Keep grade units consistent (all % or all g/t) before combining.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

Two samples:

2%

over

3 m

and

4%

over

1 m

. The length-weighted average grade is:

Q2MEDIUM2 Marks · NAT

Grades

1.5, 2.0, 3.0 g/t

over lengths

2, 3, 5 m

. The weighted average grade is ______ g/t. (Round off to two decimal places.)

g/t

Q3HARD2 Marks · NAT

Four drill intersections grade

0.8, 1.2, 1.0, 1.4%

over

5, 5, 10, 5 m

. The weighted average grade is ______ %. (Round off to two decimal places.)