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 using a three-quarter moving average, we need to calculate the average of the three most recent quarters prior to the third quarter of this year. Each quarter represents a three-month period, as described.

Here's a step-by-step breakdown:

### Step 1: Organize the Data
- **Last year:**
  - 1st quarter (Jan-Mar): 125, 145, 155
  - 2nd quarter (Apr-Jun): 195, 205, 225
  - 3rd quarter (Jul-Sep): 170, 160, 150
  - 4th quarter (Oct-Dec): 225, 250, 265
- **This year:**
  - 1st quarter (Jan-Mar): 145, 155, 140
  - 2nd quarter (Apr-Jun): 215, 230, 220
  - 3rd quarter (Jul-Sep): [Need to forecast]

### Step 2: Compute the Average for the Past 3 Quarters
We need to take the average of the last three complete quarters (4th quarter last year, 1st quarter this year, and 2nd quarter this year).

1. **4th quarter last year (Oct-Dec):** 
   - (225 + 250 + 265) / 3 = 740 / 3 = 246.67

2. **1st quarter this year (Jan-Mar):**
   - (145 + 155 + 140) / 3 = 440 / 3 = 146.67

3. **2nd quarter this year (Apr-Jun):**
   - (215 + 230 + 220) / 3 = 665 / 3 = 221.67

### Step 3: Calculate the Three-Quarter Moving Average
Now, calculate the average of these three values:

\[
\frac{246.67 + 146.67 + 221.67}{3} = \frac{615.01}{3} \approx 205.00
\]

### Forecast for the 3rd Quarter of This Year
The forecasted demand for the third quarter of this year, using a three-quarter moving average, is approximately **205 units**.

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Would you like more details or have any questions on this method?

Here are 5 additional questions you could explore:
1. How would the forecast change if using a 4-quarter moving average?
2. What are the benefits and limitations of using a moving average for forecasting?
3. How does a weighted moving average differ, and how might it affect the forecast?
4. How can the accuracy of this forecast be validated over time?
5. What are alternative methods for forecasting demand?

**Tip:** Moving averages smooth out fluctuations in data, but they may lag when trends shift quickly.

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 using a three-quarter moving average based on historical quarterly data. This problem covers key concepts in statistics and forecasting, utilizing past data from three quarters to predict future demand. Suitable for students in Grades 9-12.

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