Using a 3-month moving average, the forecast value for October made at the end of September in the following time series would be:

July

12

Aug

5

Sept

7

Oct

11

Question 4 options:

1) 

7.67

2) 

8

3) 

9

4) 

6.89

5) 

7.25

To calculate a 3-month moving average forecast for October, you need to average the values from the previous three months (July, August, and September).

Here are the values for those months:

- July: 12
- August: 5
- September: 7

The 3-month moving average forecast for October is calculated as:

\[
\text{Forecast for October} = \frac{12 + 5 + 7}{3} = \frac{24}{3} = 8
\]

So, the correct answer is:

**2) 8**

Would you like more details or have any other questions? Here are 5 related questions you might find interesting:

1. How does the length of the moving average window affect the forecast?
2. What are the limitations of using a simple moving average for forecasting?
3. How would you compute a weighted moving average, and why might it be preferred?
4. How would you adjust the moving average calculation if the data has seasonality?
5. What is the difference between a simple moving average and an exponential moving average?

**Tip:** Moving averages smooth out short-term fluctuations and highlight longer-term trends or cycles. Choosing the right window length is crucial for balancing responsiveness with smoothness.

Learn how to calculate a forecast using a 3-month moving average in time series analysis. This problem involves averaging values from July, August, and September to predict October's value. Suitable for advanced high school students and anyone interested in forecasting methods.

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