Question $2$:

The following specific percentage seasonal factors $($SF$)$ are calculated for the month of

January based on historical data: $86\mathrm{.}8\%,96\mathrm{.}9\%,72\mathrm{.}6\%,80\mathrm{.}0\%,85\mathrm{.}4\%.$ Assume

multiplicative decomposition model is used and the expected trend$-$cycle $($i$.$e$.,$ the

depersonalized data$)$ for January is $$900.$

a$)$ If the median seasonal factors is used as seasonal index $($SI$),$ then what is the

seasonal index for January?

b$)$ Assuming the SI calculated in part a$)$ is already normalized $($together with SI's

from other seasons$),$ what is the forecast for the whole year? With full calculation

c$)$ Actual sales for the year were $$12,000.$ Calculate the percentage error for the

entire year.