$\text { Construct an } \bar{x} \text { chart. }$

question 148

Essay

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

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.
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Box Weight (lb) }$
$\begin{array}{l}\begin{array}{c|}\underline {\text { Sample } }\\ 1\\2\\3\\4\\5\\6\\7\\8\\9\\10\\11\\12\\13\\14\\15\\\end{array}\begin{array}{lrll|}\\\hline 49 & 38 & 39 & 45 \\52 & 51 & 43 & 61 \\56 & 60 & 32 & 52 \\44 & 59 & 46 & 49 \\51 & 61 & 48 & 45 \\45 & 50 & 46 & 48 \\52 & 51 & 45 & 55 \\40 & 50 & 53 & 48 \\48 & 67 & 60 & 51 \\43 & 50 & 50 & 47 \\48 & 30 & 38 & 39 \\50 & 46 & 48 & 53 \\50 & 58 & 56 & 64 \\47 & 52 & 47 & 49 \\52 & 57 & 58 & 52\end{array}\begin{array}{c|}\bar{x} \\\hline 42.75 \\51.75 \\50.00 \\49.50 \\51.25 \\47.25 \\50.75 \\47.75 \\56.50 \\47.50 \\38.75 \\49.25 \\57.00 \\48.75 \\54.75\end{array}\begin{array}{c}\text { Range } \\\hline 11 \\18 \\28 \\15 \\16 \\5 \\10 \\13 \\19 \\7 \\18 \\7 \\14 \\5 \\6\end{array}\end{array}$

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