Construct a Run Chart for Individual Values Corresponding to the Given

Essay

Construct a run chart for individual values corresponding to the given data. 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. $$\begin{array} { c | c c c c | c | c } \text { Sample } & && { \text { Box Weight (Ib) } } & &\overline { \boldsymbol { x } } & \text { Range } \\\hline 1 & 49 & 38 & 39 & 45 & 42.75 & 11 \\2 & 52 & 51 & 43 & 61 & 51.75 & 18 \\3 & 56 & 60 & 32 & 52 & 50.00 & 28 \\4 & 44 & 59 & 46 & 49 & 49.50 & 15 \\5 & 51 & 61 & 48 & 45 & 51.25 & 16 \\6 & 45 & 50 & 46 & 48 & 47.25 & 5 \\7 & 52 & 51 & 45 & 55 & 50.75 & 10 \\8 & 40 & 50 & 53 & 48 & 47.75 & 13 \\9 & 48 & 67 & 60 & 51 & 56.50 & 19 \\10 & 43 & 50 & 50 & 47 & 47.50 & 7 \\11 & 48 & 30 & 38 & 39 & 38.75 & 18 \\12 & 50 & 46 & 48 & 53 & 49.25 & 7 \\13 & 50 & 58 & 56 & 64 & 57.00 & 14 \\14 & 47 & 52 & 47 & 49 & 48.75 & 5 \\15 & 52 & 57 & 58 & 52 & 54.75 & 6\end{array}$$