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$\backslash$begin$\{$tabular$\}\{$ccccc$\}$

$\backslash$multicolumn$\{5\}\{$c$\}\{$ Bottle $\}\backslash \backslash$

$\backslash$hline Sample & $\backslash (\backslash$mathbf$\{1\}\backslash )$ & $\backslash (\backslash$mathbf$\{2\}\backslash )$ & $\backslash (\backslash$mathbf$\{3\}\backslash )$ & $4\backslash \backslash$

$\backslash$hline $1$ & $0\mathrm{.}582$ & $0\mathrm{.}582$ & $0\mathrm{.}582$ & $0\mathrm{.}607\backslash \backslash$

$2$ & $0\mathrm{.}588$ & $0\mathrm{.}583$ & $0\mathrm{.}592$ & $0\mathrm{.}596\backslash \backslash$

$3$ & $0\mathrm{.}579$ & $0\mathrm{.}618$ & $0\mathrm{.}610$ & $0\mathrm{.}576\backslash \backslash$

$4$ & $0\mathrm{.}610$ & $0\mathrm{.}589$ & $0\mathrm{.}570$ & $0\mathrm{.}608\backslash \backslash$

$5$ & $0\mathrm{.}578$ & $0\mathrm{.}620$ & $0\mathrm{.}578$ & $0\mathrm{.}575\backslash \backslash$

$6$ & $0\mathrm{.}615$ & $0\mathrm{.}615$ & $0\mathrm{.}614$ & $0\mathrm{.}607\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Click the icon to view the table of factors for calculating three$-$sigma limits for the $\backslash (\backslash$bar$\{$x$\}\backslash )-$chart and R $-$chart.

More Info

Assume that only these six samples are sufficient, and use the data to determine control limits for an R $-$ and an $\backslash (\backslash$overline$\{\backslash$mathrm$\{$x$\}\}\backslash )-$chart.

Compute the range R and the sample mean $\backslash (\backslash$overline$\{\backslash$mathrm$\{$x$\}\}\backslash )$ for each sample. $($Enter your responses rounded to three decimal places.$)$

$\backslash$begin$\{$tabular$\}\{$ccccccc$\}$

$\backslash$hline & $\backslash$multicolumn$\{5\}\{$c$\}\{$ Bottle $\}$ & $\backslash \backslash$

$\backslash$cline $\{2-5\}$ Sample & $\backslash (\backslash$mathbf$\{1\}\backslash )$ & $\backslash (\backslash$mathbf$\{2\}\backslash )$ & $\backslash (\backslash$mathbf$\{3\}\backslash )$ & $\backslash (\backslash$mathbf$\{4\}\backslash )$ & $\backslash (\backslash$mathbf$\{$R$\}\backslash )$ & $\backslash (\backslash$overline$\{\backslash$mathbf$\{$x$\}\}\backslash )\backslash \backslash$

$\backslash$hline $1$ & $0\mathrm{.}582$ & $0\mathrm{.}582$ & $0\mathrm{.}582$ & $0\mathrm{.}607$ & $0\mathrm{.}025$ & $0\mathrm{.}588\backslash \backslash$

$2$ & $0\mathrm{.}588$ & $0\mathrm{.}583$ & $0\mathrm{.}592$ & $0\mathrm{.}596$ & $0\mathrm{.}013$ & $0\mathrm{.}590\backslash \backslash$

$3$ & $0\mathrm{.}579$ & $0\mathrm{.}618$ & $0\mathrm{.}610$ & $0\mathrm{.}576$ & $0\mathrm{.}042$ & $0\mathrm{.}596\backslash \backslash$

$4$ & $0\mathrm{.}610$ & $0\mathrm{.}589$ & $0\mathrm{.}570$ & $0\mathrm{.}608$ & $0\mathrm{.}040$ & $0\mathrm{.}594\backslash \backslash$

$5$ & $0\mathrm{.}578$ & $0\mathrm{.}620$ & $0\mathrm{.}578$ & $0\mathrm{.}575$ & $1$ & $1\backslash \backslash$

$6$ & $0\mathrm{.}615$ & $0\mathrm{.}615$ & $0\mathrm{.}614$ & $0\mathrm{.}607$ & $1$ & $1\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

The $\backslash ($ U C L$\_\{$R$\}\backslash )$ equals $1$ inches and the $\backslash ($ L C L$\_\{$R$\}\backslash )$ equals inches. $($Enter your responses rounded to three decimal places. If your answer for $\backslash (\backslash$mathrm$\{$LCL$\}\_\{\backslash$mathrm$\{$R$\}\}\backslash )$ is negative, enter this value as $0.)$

The $\backslash ($ U C L$\_\{-\}^\{-\}\backslash )$equals $1$ inches and the $\backslash (\backslash$mathrm$\{$LCL$\}\_\{\backslash$overline$\{-\}\}\backslash )$ equals inches. $($Enter your responses rounded to three decimal places.$)$