Division 3.2.4 Calculation of the mean value x — and of the average range of R — of the 40 measuring container bottles in the sample.

to obtain $\stackrel{—}{x}$ , calculate as follows:

• the sum of the 40 actual capacity measurements x_i: Σ x_i

• the mean value of these 40 measurements: $\stackrel{—}{x}=\frac{{\mathrm{\Sigma x}}_i}{40}$

To obtain $\stackrel{—}{R}:$

Divide the sample, in chronological order of selection, into eight sub-samples of five measuring container bottles each.

Calculate as follows:

• the range of each of the sub-samples, i.e. the difference between the actual capacity of the largest and the smallest of the five bottles in the sub-sample; eight ranges are thus obtained: R₁; R₂; ... R₈

• the sum of the ranges of the eight sub-samples:

  Σ R_i = R₁ + ${\stackrel{—}{R}}_2$ + ... + R₈

The average range $\stackrel{—}{R}$ is therefore: $\stackrel{—}{R}=\frac{{\mathrm{\Sigma R}}_i}{8}$