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The details of the clock sales at a supermarket for the past 6 weeks are shown in the table below. The time series appears to be relatively stable, without trend, seasonal, or cyclical effects. The simple moving average value of [tex]k[/tex] is set at 3.

\begin{tabular}{c|c|}
Week & Units Sold \\
\hline
1 & 88 \\
\hline
2 & 44 \\
\hline
3 & 54 \\
\hline
4 & 65 \\
\hline
5 & 72 \\
\hline
6 & 85 \\
\hline
\end{tabular}

Using the data, determine the value of the three-period moving average forecast for week 4.



Answer :

GinnyAnswer
Certainly! Let's determine the three-period moving average forecast for week 4 based on the given sales data for the past 6 weeks.

The data provided is as follows:

[tex]\[ \begin{array}{|c|c|} \hline \text{Week} & \text{Units Sold} \\ \hline 1 & 88 \\ \hline 2 & 44 \\ \hline 3 & 54 \\ \hline 4 & 65 \\ \hline 5 & 72 \\ \hline 6 & 85 \\ \hline \end{array} \][/tex]

To calculate the three-period moving average forecast for week 4, we'll take the average of the units sold in the previous three weeks (i.e., weeks 1, 2, and 3).

Here are the steps for the calculation:

1. Identify the units sold for weeks 1, 2, and 3:
[tex]\[ \text{Units sold in week 1} = 88 \][/tex]
[tex]\[ \text{Units sold in week 2} = 44 \][/tex]
[tex]\[ \text{Units sold in week 3} = 54 \][/tex]

2. Calculate the sum of the units sold in these three weeks:
[tex]\[ \text{Sum} = 88 + 44 + 54 = 186 \][/tex]

3. Compute the average by dividing the sum by the number of weeks (3):
[tex]\[ \text{Three-period moving average forecast for week 4} = \frac{186}{3} = 62.0 \][/tex]

Therefore, the three-period moving average forecast for week 4 is [tex]\(62.0\)[/tex].

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