Data for use in constructing a control chart have been collected on the time $($in seconds$)$ to perform a particular task. Six samples were collected in the afternoon and the times are shown below:

Time Time in seconds

$1$:$00$ PM $76808280$

$1$:$30$ PM $82798483$

$2$:$00$ PM $75827883$

$2$:$30$ PM $73767881$

$3$:$00$ PM $77788478$

$3$:$30$ PM $78798079$

Determine the upper and lower control limits for a $($three$-$sigma$)$ X $$ chart. Show all your work.

Upper control limit $=\_\_\_\_\_\_\_\_\_\_\_$

Lower control limit $=\_\_\_\_\_\_\_\_\_\_$