c̄ = Σ(mᵢ cᵢ) / Σmᵢmᵢ: mass d’a fraction; cᵢ: content of this fraction.
Use when: Weighted average; use the same wet or dry base for all masses.
Representative sampling and quartering
Distinguish a reduction in mass from an involuntary selection of particles.
What is happening?
A mining lot is heterogeneous: content, size and density vary between particles. Sampling aims to give fractions of the lot a fair chance of being represented.
Quarting reduces the mass after mixing and distribution. Taking only large grains, fines or the surface of the pile creates a bias that repeated analyzes do not correct.
The formulas, with their conditions.
mfinale ≈ m₀ / 2ᵏk: number of divisions into two comparable fractions.
Use when: Ideal mass reduction; does not alone guarantee representativeness.
Where is this principle used?
Mining laboratory and concentration plant
Prepare a test portion for content analysis.
Control of deliveries
Characterize a batch before processing or sale.
What to observe in the experiment
Compare selective sampling and sharing after homogenization. Examine the dispersion of the contents obtained.
References and readings
This sheet explains the principles and their assumptions. Educational simulation can simplify the process; an industrial model requires suitable data and validation.
Have you understood the essentials?
Only one correct answer per question. Answer all three questions, then view the answer key.
Intu Lab · Understanding sheet · Kimba Christian