One hotel has average customer rating $(0-10)$ from January to June as $7\mathrm{.}7,7\mathrm{.}5,$

$8\mathrm{.}1.7\mathrm{.}8.8\mathrm{.}2.7\mathrm{.}4.$ Since July $1,$ a new hotel manager has been appointed, with

average customer rating from July to December as $7\mathrm{.}9,7\mathrm{.}6,8\mathrm{.}3,8\mathrm{.}1,7\mathrm{.}8,8\mathrm{.}4.$

$($a$)$ Do you consider any improvement of hotel service under this new hotel

manager? Why?

$($b$)\backslash$Vhat is your prediction of the average customer rating in January next

year? Please quantitively explain your reasoning.