Given the following history, use a three-quarter moving average to forecast the demand for the third quarter of this year. Note, the 1st quarter is Jan, Feb, and Mar; 2nd quarter Apr, May, Jun; 3rd quarter Jul, Aug, Sep; and 4th quarter Oct, Nov, Dec.

 

 	JAN	FEB	MAR	APR	MAY	JUN	JUL	AUG	SEP	OCT	NOV	DEC
Last year	125	145	155	195	205	225	170	160	150	225	250	265
This year	145	155	140	215	230	220	 	 	 	 	 	

To forecast the demand for the third quarter of this year (July, August, and September) using a **three-quarter moving average**, we need to take the average demand of the previous three quarters (1st quarter, 2nd quarter, and 4th quarter of last year) to project the demand for the 3rd quarter of this year.

Here's a breakdown of the steps:

### Data Given:

- **Last Year**:
  - 1st Quarter: Jan = 125, Feb = 145, Mar = 155
  - 2nd Quarter: Apr = 195, May = 205, Jun = 225
  - 3rd Quarter: Jul = 170, Aug = 160, Sep = 150
  - 4th Quarter: Oct = 225, Nov = 250, Dec = 265

- **This Year**:
  - 1st Quarter: Jan = 145, Feb = 155, Mar = 140
  - 2nd Quarter: Apr = 215, May = 230, Jun = 220
  - 3rd Quarter: Jul = (forecast), Aug = (forecast), Sep = (forecast)

### Step 1: Calculate the Total Demand for Each Quarter
- **Last Year 1st Quarter**: \( 125 + 145 + 155 = 425 \)
- **Last Year 2nd Quarter**: \( 195 + 205 + 225 = 625 \)
- **Last Year 4th Quarter**: \( 225 + 250 + 265 = 740 \)

- **This Year 1st Quarter**: \( 145 + 155 + 140 = 440 \)
- **This Year 2nd Quarter**: \( 215 + 230 + 220 = 665 \)

### Step 2: Calculate the Three-Quarter Moving Average
For the forecast of the 3rd quarter of this year, we use the total demand from the last three quarters (i.e., 1st and 2nd quarters of this year, and 4th quarter of last year):

\[
\text{Three-quarter Moving Average} = \frac{440 + 665 + 740}{3} = \frac{1845}{3} = 615
\]

### Step 3: Forecast for the 3rd Quarter of This Year
The forecasted demand for the 3rd quarter of this year is **615** units.

Would you like more details or clarification on any part of this process?

Here are some related questions you might find helpful:
1. How does the choice of different moving averages (e.g., two-quarter, four-quarter) affect the forecast?
2. What are the advantages of using a moving average for forecasting demand?
3. How could seasonality adjustments improve the accuracy of this forecast?
4. Can other methods like exponential smoothing be more effective in certain forecasting scenarios?
5. How would you forecast demand for future quarters using this method?

**Tip:** Moving averages work well when there's no strong trend or seasonal pattern in the data, but may lag in detecting sudden changes.

Given the following history, use a three-quarter moving average to forecast the demand for the third quarter of this year. Note, the 1st quarter is Jan, Feb, and Mar; 2nd quarter Apr, May, Jun; 3rd quarter Jul, Aug, Sep; and 4th quarter Oct, Nov, Dec.

Learn how to forecast demand for the third quarter of this year using a three-quarter moving average. This solution involves time series analysis, calculating the average demand from previous quarters, and is suitable for students in Grades 10-12.

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