Assume that only these six samples are$$ sufficient, and use the data to determine control limits for an$$ R$-$ and an x overbar$-$chart.

Compute the range R and the sample mean x overbar for each sample. $($Enter your responses rounded to three decimal places$.)$

Bottle

Sample

$1$

$2$

$3$

$4$

R

x overbar

$1$

$0\mathrm{.}597$

$0\mathrm{.}602$

$0\mathrm{.}619$

$0\mathrm{.}597$

$0\mathrm{.}022$

$0\mathrm{.}604$

$2$

$0\mathrm{.}618$

$0\mathrm{.}581$

$0\mathrm{.}621$

$0\mathrm{.}590$

$0\mathrm{.}040$

$0\mathrm{.}603$

$3$

$0\mathrm{.}613$

$0\mathrm{.}624$

$0\mathrm{.}604$

$0\mathrm{.}606$

$0\mathrm{.}020$

$0\mathrm{.}612$

$4$

$0\mathrm{.}613$

$0\mathrm{.}582$

$0\mathrm{.}595$

$0\mathrm{.}623$

$0\mathrm{.}041$

$0\mathrm{.}603$

$5$

$0\mathrm{.}621$

$0\mathrm{.}599$

$0\mathrm{.}593$

$0\mathrm{.}592$

$$

$0\mathrm{.}029$

$$

$0\mathrm{.}601$

$6$

$0\mathrm{.}621$

$0\mathrm{.}612$

$0\mathrm{.}611$

$0\mathrm{.}579$

$$

$0\mathrm{.}042$

$$

$0\mathrm{.}606$

Part $3$

The UCL Subscript Upper R equals

$$

enter your response here inches and the LCL Subscript Upper R equals

$$

enter your response here inches. $($Enter your responses rounded to three decimal places. If your answer for LCL Subscript Upper R is$$ negative, enter this value as $0.)$

Click the icon to view the table of factors for calculating three$-$sigma limits for the x overbar$-$chart and R$-$chart.Click the icon to view the table of factors for calculating three$-$sigma limits for the x overbar$-$chart and R$-$chart.Click the icon to view the table of factors for calculating three$-$sigma limits for the x overbar$-$chart and R$-$chart.Click the icon to view the table of factors for calculating three$-$sigma limits for the x overbar$-$chart and R$-$chart.The UCL Subscript Upper R equalsLCL Subscript Upper Rinches and the LCL Subscript Upper R equalsLCL Subscript Upper R