To determine the three-period moving average for the next time period, we need to follow these steps:
1. Identify the Data Points:
We have the monthly profits for an auto repair shop for nine months, from January 2014 to September 2014:
- Jan-14: [tex]$16,012
- Feb-14: $[/tex]16,162
- Mar-14: [tex]$14,955
- Apr-14: $[/tex]17,016
- May-14: [tex]$18,663
- Jun-14: $[/tex]17,200
- Jul-14: [tex]$19,142
- Aug-14: $[/tex]18,457
- Sep-14: [tex]$20,242
2. Select the Last Three Data Points:
To find the three-period moving average for the next period (October-14), we need the most recent three profits:
- Jul-14: $[/tex]19,142
- Aug-14: [tex]$18,457
- Sep-14: $[/tex]20,242
3. Calculate the Sum of the Last Three Profits:
Sum these three values to obtain the total profit over the last three months:
[tex]\[
19,142 + 18,457 + 20,242 = 57,841
\][/tex]
4. Compute the Moving Average:
To find the three-period moving average, divide the total sum by 3:
[tex]\[
\frac{57,841}{3} = 19,280.3333\ldots
\][/tex]
5. Round to One Decimal Place:
Finally, round the result to one decimal place:
[tex]\[
19,280.3
\][/tex]
Therefore, the three-period moving average for the next time period is 19,280.3.
