Problem $5(20$ Points$)$

The ChatCamp Outdoor Company is a catalog sales operation that specializes in outdoor recreational clothing. Demand for its items is very seasonal, peaking during the Christmas season and during the spring. It has accumulated the following data for orders per season $($quarter$)$ during the past $5$ years:

$\backslash$table$[[$Quarter$,$Orders $\frac{1,000s}{?}$ Year,$\backslash$table$[[$Average$],[$Demad per$],[$Quarter$]],\backslash$table$[[$Seasonal$],[$Index$]]],[1,2,3,4,5],[$Jan$-$Mar,$27\mathrm{.}50,28\mathrm{.}50,37\mathrm{.}50,42\mathrm{.}50,49\mathrm{.}50,,],[$Apr $-$ Jun,$26\mathrm{.}75,31\mathrm{.}75,34\mathrm{.}75,42\mathrm{.}75,44\mathrm{.}75,,],[$Jul $-$ Sep,$29\mathrm{.}00,32\mathrm{.}00,41\mathrm{.}00,44\mathrm{.}00,48\mathrm{.}00,,],[$Oct$-$Dec,$27\mathrm{.}25,32\mathrm{.}25,42\mathrm{.}25,47\mathrm{.}25,53\mathrm{.}25,,]]$

a$.$ Calculate the overall average demad.

b$.$ Calculate the average demad per quarter in the space given in the above table.

c$.$ Calculate the seasonal index in the space given in the above table.