At the EXO Hotel, manager Kai collected extremely precise data in minutes on check$-$in times using a sample $($sub$-$group$)$ of $6$ check$-$ins per day over a period of $30$ days. An excerpt of that data, consisting of the first $3$ days of data, are shown below $($no Excel file and no calculations needed for this question$).$

Observations

$1$

$2$

$3$

$4$

$5$

$6$

Day $1$

$6\mathrm{.}00$

$4\mathrm{.}33$

$7\mathrm{.}33$

$7\mathrm{.}00$

$6\mathrm{.}00$

$5\mathrm{.}00$

Day $2$

$5\mathrm{.}75$

$8\mathrm{.}25$

$2\mathrm{.}33$

$4\mathrm{.}25$

$5\mathrm{.}75$

$7\mathrm{.}50$

Day $3$

$7\mathrm{.}00$

$7\mathrm{.}75$

$6\mathrm{.}75$

$6\mathrm{.}25$

$7\mathrm{.}00$

$6\mathrm{.}50$

Kai would like your help in identifying what control chart$($s$)$ to use.

Please identify and report the type of control chart$($s$)$ that would be appropriate if this data $($for all $30$ days$)$ is available, and provide a one$-$sentence justification for the same.

Describe in words how you would go about calculating the Center Line$($s$)$ for the control chart$($s$)$ including what you would need to get from each of the $30$ samples individually and from all $30$ samples together.