Estimates the mean and the standard deviation, μ, σ, of a (Gaussian) random variable from sums of the values of unequal (or equal) size samples. (The summands are, thus, assumed not known.) A typical case are trucks of different sizes loaded with bags, the bag being the item with random weight. (The base data are inspired in real bags of fertilizers.)

Simulated values are used, from a Gaussian with given parameters mean and standard deviation, μ and σ. (Here, the values are weights of bags or other additive values.)

There are T samples ("T" as in "truck"), and the sample sizes are n_i, i = 1..T, in the given vector n. (The samples are, indeed, commercial batches or lots.)

The procedure estimates μ (which is trivial) and σ from a set of experimental data that are here simulated but which routinely exist in many industries.

The computation being lengthy, if the number of trials is excessive (for the total lot sizes), it is reduced (trials × N ≤ 10⁸).

Draws a plot of f, the 'pdf', and F, the 'cdf', of the variable simulated: weighted average (around μ); or variance (around σ²).

• Google search: "different sample size" -unequal; "unequal sample size" -different

• Catálogo de fertilizantes (ADP fertilizantes, SA, "fertilizers"). (SAPEC; Tradecorp)

• SPE 2019, XXIV Congresso da Sociedade Portuguesa de Estatística (24.^th Congress of the Portuguese Society of Statistics), 06–09 Novembro 2019, Amarante (Porto, Portugal)

• 1872-12-23: Pfeiffer, Georgii (Yurii) Vasilyovich (Георгій Васильович Пфейффер) (Ukr., Wikip.; Convert Jul. Greg. cal.) († 1946-10-10).