You are given the following budgeted and actual data for the Grey Company for each of the months January through June of the

current year.

In December of the prior year, sales were forecasted as follows: January, $99$ units; February, $94$ units; March, $101$ units; April, $106$ units;

May, $113$ units; June, $121$ units. In January of the current year, sales for the months February through June were reforecasted as follows:

February, $89$ units; March, $101$ units; April, $101$ units; May, $103$ units; June, $116$ units. In February of the current year, sales for the months

March through June were reforecasted as follows: March, $96$ units; April, $101$ units; May, $98$ units; June, $116$ units. In March of the

current year, sales for the months April through June were reforecasted as follows: April, $101$ units; May, $93$ units; June, $106$ units. In

April of the current year, sales for the months May and June were reforecasted as follows: May, $83$ units; June, $101$ units. In May of the

current year, sales for June were reforecasted as $101$ units.

Actual sales for the six$-$month period, January through June, were as follows: January, $94$ units; February, $89$ units; March, $103$ units;

April, $109$ units; May, $118$ units; June, $115$ units.

Required:

Prepare a schedule of forecasted sales, on a rolling basis, for the months January through June, inclusive. $($Hint: There will be only

one forecasted number for January$-$this is the forecast done in December. For February, there will be two forecasts: one done in

December and a second done in January. For June, there will be six forecasts, one done in each of the preceding six months.$)$

For each of the months March through June, determine the $3-$month forecast error rate, defined as $1$ minus the absolute percentage

error. For example, the forecast error rate for March's sales is found by dividing the absolute value of the forecast error for this month

by the actual sales volume for the month. The forecast error for any month $($e$.$g$.,$ March$)$ is defined as the difference between the actual

sales volume for the month and the sales volume for that month forecasted $3$ months earlier $($e$.$g$.,$ December$).$ Also, indicate for each

month whether the actual sales volume was above or below the forecasted volume generated three months earlier.