 Composite sample

ID: composite-sample

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Codex  0 2026-11-05

A composite sample is formed by combining material from several collected portions into one mixture, from which material for laboratory measurement is taken. It can represent an aggregate composition when the collection and mixing weights match the intended target. IUPAC describes compositing as preparation of a mixture from several samples; combining them does not by itself prove representativeness.^[ref]

Suppose sampling increments have masses

m_{i}

and analyte mass fractions

c_{i}

. With complete transfer, no chemical change and adequate mixing, conservation of analyte gives

c_{comp} = \frac{\sum _{i} m _{i} c _{i}}{\sum _{i} m _{i}} = \sum_{i} w_{i} c_{i}, w_{i} = \frac{m _{i}}{\sum _{j} m _{j}} .

(1)

Equal increment masses produce an arithmetic mean; unequal masses produce a mass-weighted mean. Weights chosen to represent different parts of the sampling target can differ from the fractions accidentally collected.

An original example shows what is lost. Four equal-mass portions with concentrations

(0, 0, 0, 40)

milligrams per kilogram give the same composite concentration, 10 milligrams per kilogram, as portions with concentrations

(10, 10, 10, 10)

. A single composite measurement cannot distinguish a localized high value from uniform composition. It addresses the weighted average, not the maximum or the spatial distribution.

The uncertainty of that average depends on dependence between portions. For a random concentration vector with covariance matrix

Σ

and fixed mixing weights,

Var (c_{comp}) = w^{T} Σ w .

(2)

For four equal-weight portions each with standard deviation 2 concentration units and common pairwise correlation coefficient 0.25, this gives

Var (c_{comp}) = \frac{4 ( 4 ) + 12 ( 1 )}{16} = 1.75,

(3)

and standard deviation about 1.32 units. Assuming independence would instead give 1 unit. This stipulated model concerns collected-material variation; common losses or measurement errors can add other contributions.^[ref]

A practical protocol specifies increment selection, mixing proportions, mixing procedure and reduction to a test portion. Loss of volatile material, segregation of particles or incomplete mixing can make the analysed portion differ from the intended composite. Replicate readings of one final solution test later measurement stages; independent composites are needed to investigate variability introduced during collection and pooling.

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