Four Samples of Three Observations Each Have Been Taken, with Actual

Essay

Four samples of three observations each have been taken, with actual measurements (in centimeters) shown below. Construct three-sigma mean and range charts. $\begin{array}{ccrc}\text { Sample }\\\begin{array}{ccrc}\hline 1 & 2 & 3 & 4 \\12.3 & 11.9 & 12.0 & 12.1 \\12.2 & 12.2 & 12.2 & 11.8 \\12.1 & 12.2 & 11.8 & 11.8\end{array}\end{array}$

$\begin{array}{ccccc}\text { Sample } & 1 & 2 & 3 & 4 \\\text { Mean } & 12.2 & 12.1 & 12.0 & 11.9 \\\text { Range } & .2 & .3 & 4 & .3\end{array}$

$\text { Grand mean }=12.05 ; \text { R-bar }=0.3$