The following table contains the measurements of the key length dimension from a fuel injector. These samples of size five we taken at one$-$hour intervals. Use three$-$sigma control limits$.$ Use Exhibit $10\mathrm{.}13.$

$\backslash$table$[[,$OBSERVATIONS$],[$SAMPLE$,],[$NUMBER$,1,2,3,4,5],[1,0\mathrm{.}485,0\mathrm{.}482,0\mathrm{.}483,0\mathrm{.}507,0\mathrm{.}486],[2,0\mathrm{.}498,0\mathrm{.}503,0\mathrm{.}519,0\mathrm{.}492,0\mathrm{.}523],[3,0\mathrm{.}495,0\mathrm{.}485,0\mathrm{.}512,0\mathrm{.}485,0\mathrm{.}521],[4,0\mathrm{.}494,0\mathrm{.}503,0\mathrm{.}483,0\mathrm{.}482,0\mathrm{.}483],[5,0\mathrm{.}471,0\mathrm{.}499,0\mathrm{.}525,0\mathrm{.}461,0\mathrm{.}487],[6,0\mathrm{.}472,0\mathrm{.}484,0\mathrm{.}504,0\mathrm{.}483,0\mathrm{.}496],[7,0\mathrm{.}498,0\mathrm{.}513,0\mathrm{.}482,0\mathrm{.}471,0\mathrm{.}506],[8,0\mathrm{.}522,0\mathrm{.}498,0\mathrm{.}492,0\mathrm{.}472,0\mathrm{.}495],[9,0\mathrm{.}493,0\mathrm{.}503,0\mathrm{.}517,0\mathrm{.}506,0\mathrm{.}512],[10,0\mathrm{.}494,0\mathrm{.}504,0\mathrm{.}519,0\mathrm{.}507,0\mathrm{.}493],[11,0\mathrm{.}495,0\mathrm{.}483,0\mathrm{.}462,0\mathrm{.}482,0\mathrm{.}488],[12,0\mathrm{.}479,0\mathrm{.}451,0\mathrm{.}513,0\mathrm{.}506,0\mathrm{.}523],[13,0\mathrm{.}521,0\mathrm{.}513,0\mathrm{.}483,0\mathrm{.}524,0\mathrm{.}511],[14,0\mathrm{.}484,0\mathrm{.}524,0\mathrm{.}504,0\mathrm{.}507,0\mathrm{.}501],[15,0\mathrm{.}493,0\mathrm{.}519,0\mathrm{.}493,0\mathrm{.}507,0\mathrm{.}512],[16,0\mathrm{.}474,0\mathrm{.}503,0\mathrm{.}472,0\mathrm{.}483,0\mathrm{.}517],[17,0\mathrm{.}464,0\mathrm{.}485,0\mathrm{.}504,0\mathrm{.}485,0\mathrm{.}492],[18,0\mathrm{.}518,0\mathrm{.}483,0\mathrm{.}483,0\mathrm{.}486,0\mathrm{.}472],[19,0\mathrm{.}512,0\mathrm{.}527,0\mathrm{.}482,0\mathrm{.}493,0\mathrm{.}482],[20,0\mathrm{.}509,0\mathrm{.}482,0\mathrm{.}473,0\mathrm{.}506,0\mathrm{.}513]]$

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