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 January, February, and March; 2nd quarter April, May, June; 3rd quarter July, August, September; and 4th quarter October, November, December.

JANUARY	FEBRUARY	MARCH	APRIL	MAY	JUNE	JULY	AUGUST	SEPTEMBER	OCTOBER	NOVEMBER	DECEMBER
Last year	125	140	150	190	200	225	165	155	145	225	250	275
This year	140	150	170	205	230	260	0	0	0	0	0	0

To forecast the demand for the third quarter of this year using a three-quarter moving average, we first calculate the average of the most recent three quarters. Since the data provided includes values up to the second quarter of this year, we will use the last three quarters with completed data, which are:

1. **4th Quarter of Last Year** (October, November, December): 225, 250, 275
2. **1st Quarter of This Year** (January, February, March): 140, 150, 170
3. **2nd Quarter of This Year** (April, May, June): 205, 230, 260

**Steps:**

1. First, calculate the total demand for each of these quarters, and then find the average demand for each quarter.
2. Finally, take the average of these three quarterly averages to find the forecast for the third quarter of this year.

### Step 1: Calculate the Quarterly Averages
1. **4th Quarter of Last Year**:  
   \[
   \text{Average} = \frac{225 + 250 + 275}{3} = \frac{750}{3} = 250
   \]

2. **1st Quarter of This Year**:  
   \[
   \text{Average} = \frac{140 + 150 + 170}{3} = \frac{460}{3} \approx 153.33
   \]

3. **2nd Quarter of This Year**:  
   \[
   \text{Average} = \frac{205 + 230 + 260}{3} = \frac{695}{3} \approx 231.67
   \]

### Step 2: Calculate the Three-Quarter Moving Average
\[
\text{Three-Quarter Moving Average} = \frac{250 + 153.33 + 231.67}{3} = \frac{635}{3} \approx 211.67
\]

### Forecast for the Third Quarter of This Year
The forecasted demand for the third quarter of this year is approximately **211.67**.

Would you like a breakdown of the calculations or have questions about this process?

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Here are 5 related questions to further your understanding:

1. How would the forecast change if a different moving average period was used?
2. What would be the effect of including only the last two quarters in the moving average?
3. How does a weighted moving average differ from a simple moving average?
4. Why might a company prefer to use moving averages for forecasting instead of other methods?
5. How would you adjust if there were missing data for one of the months?

**Tip:** Moving averages smooth out fluctuations in data, making trends clearer, especially in cases with seasonal or irregular patterns.

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 January, February, and March; 2nd quarter April, May, June; 3rd quarter July, August, September; and 4th quarter October, November, December.

JANUARY FEBRUARY MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER DECEMBER
Last year 125 140 150 190 200 225 165 155 145 225 250 275
This year 140 150 170 205 230 260 0 0 0 0 0 0

Learn how to forecast demand for the third quarter using a three-quarter moving average. This solution provides a step-by-step breakdown, using historical data from last year and this year's Q1 and Q2, to project Q3 demand. Suitable for high school students learning forecasting techniques.

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