To set up the machine and to create a control chart to be used throughout the run, $15$ samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows: Use three$-$sigma control limits as in Exhibit $13\mathrm{.}7.$

$\backslash$table$[[\backslash$table$[[$SAMPLE$],[$NUMBER$]],$READINGS,$($IN OHMS$)],[1,972,997,1032,972],[2,1024,1029,979,1024],[3,1002,1014,1007,1030],[4,981,1028,994,974],[5,983,1023,1025,988],[6,985,990,1019,979],[7,980,1002,995,991],[8,1011,1027,985,1004],[9,999,979,973,1022],[10,1019,983,974,996],[11,978,1018,979,984],[12,1002,974,985,984],[13,1030,1023,1004,1017],[14,995,998,997,1016],[15,973,983,1011,977]]$

a$.$ Calculate the mean and range for the above samples.

Note: Round "Mean" to $2$ decimal places and "Range" to the nearest whole number.

$\backslash$table$[[$Sample Number,Mean,Range$],[1,993\mathrm{.}25,60],[2,1,014\mathrm{.}00,50],[3,1,013\mathrm{.}25,28],[4,994\mathrm{.}25,47],[5,1,004\mathrm{.}75,42],[6,993\mathrm{.}25,40],[7,992\mathrm{.}00,22],[8,1,006\mathrm{.}75,42],[9,993\mathrm{.}25,49],[10,993\mathrm{.}00,45],[11,989\mathrm{.}75,40],[12,986\mathrm{.}25,28],[13,1,018\mathrm{.}50,26],[14,1,001\mathrm{.}50,21],[15,986\mathrm{.}00,38]]$

b$.$ Determine $\stackrel{}{x}$ and $\frac{?}{\text{b}\text{a}\text{r}}(R).$

Note: Round your answers to $3$ decimal places.

$\backslash$table$[[x,1,003\mathrm{.}687$