Construct An $\bar { x }$ Chart
Control Chart Constants A Machine Is Supposed to Fill Boxes to a Weight

Essay

Construct an $\bar { x }$ chart.
Control Chart Constants
$\begin{array}{ccccccc}&\bar{x}&&s&&R\\\hline n & A_{2} & A_{3} & B_{3} & B_{4} & D_{3} & D_{4} \\\hline 2 & 1.880 & 2.659 & 0.000 & 3.267 & 0.000 & 3.267 \\3 & 1.023 & 1.954 & 0.000 & 2.568 & 0.000 & 2.574 \\4 & 0.729 & 1.628 & 0.000 & 2.266 & 0.000 & 2.282 \\5 & 0.577 & 1.427 & 0.000 & 2.089 & 0.000 & 2.114 \\6 & 0.483 & 1.287 & 0.030 & 1.970 & 0.000 & 2.004 \\7 & 0.419 & 1.182 & 0.118 & 1.882 & 0.076 & 1.924 \\8 & 0.373 & 1.099 & 0.185 & 1.815 & 0.136 & 1.864 \\9 & 0.337 & 1.032 & 0.239 & 1.761 & 0.184 & 1.816 \\10 & 0.308 & 0.975 & 0.284 & 1.716 & 0.223 & 1.777 \\\hline\end{array}$

A machine is supposed to fill boxes to a weight of 50 pounds. Every 30 minutes a sample of four boxes is tested; the results are given below.
$\begin{array} { c | c c c c | c | c } \text { Sample } &&& { \text { Beight (lb) } } && \overline { \boldsymbol { x } } & \text { Range } \\\hline 1 & 49 & 38 & 39 & 45 & 42.75 & 11 \\2 & 52 & 51 & 43 & 61 & 51.75 & 18 \\3 & 56 & 60 & 32 & 52 & 50.00 & 28 \\4 & 44 & 59 & 46 & 49 & 49.50 & 15 \\5 & 51 & 61 & 48 & 45 & 51.25 & 16 \\6 & 45 & 50 & 46 & 48 & 47.25 & 5 \\7 & 52 & 51 & 45 & 55 & 50.75 & 10 \\8 & 40 & 50 & 53 & 48 & 47.75 & 13 \\9 & 48 & 67 & 60 & 51 & 56.50 & 19 \\10 & 43 & 50 & 50 & 47 & 47.50 & 7 \\11 & 48 & 30 & 38 & 39 & 38.75 & 18 \\12 & 50 & 46 & 48 & 53 & 49.25 & 7 \\13 & 50 & 58 & 56 & 64 & 57.00 & 14 \\14 & 47 & 52 & 47 & 49 & 48.75 & 5 \\15 & 52 & 57 & 58 & 52 & 54.75 & 6\end{array}$