Question 1200719
**1. Calculate the Average Sales for Each Season**

* **Season 1:** (1856 + 1995 + 2241 + 2280) / 4 = 2093
* **Season 2:** (2012 + 2168 + 2306 + 2408) / 4 = 2223.5
* **Season 3:** (985 + 1072 + 1105 + 1120) / 4 = 1070.5

**2. Calculate the Average Sales for Each Year**

* **Year 1:** (1856 + 2012 + 985) / 3 = 1617.67
* **Year 2:** (1995 + 2168 + 1072) / 3 = 1745
* **Year 3:** (2241 + 2306 + 1105) / 3 = 1884
* **Year 4:** (2280 + 2408 + 1120) / 3 = 1936

**3. Calculate the Centered Moving Average (CMA)**

* **Calculate 4-year moving averages:** 
    * (Year 1 + Year 2) / 2 = (1617.67 + 1745) / 2 = 1681.335
    * (Year 2 + Year 3) / 2 = (1745 + 1884) / 2 = 1814.5
    * (Year 3 + Year 4) / 2 = (1884 + 1936) / 2 = 1910

* **Calculate Centered Moving Averages:**
    * (1681.335 + 1814.5) / 2 = 1747.9175 
    * (1814.5 + 1910) / 2 = 1862.25

**4. Calculate the Ratio-to-Moving-Average (RMA)**

* Divide the actual sales for each period by the corresponding centered moving average.

| Year | Season | Sales | CMA | RMA |
|---|---|---|---|
| 1 | 1 | 1856 | 1747.9175 | 1.062 |
| 1 | 2 | 2012 | 1747.9175 | 1.151 |
| 1 | 3 | 985 | 1747.9175 | 0.563 |
| 2 | 1 | 1995 | 1747.9175 | 1.141 |
| 2 | 2 | 2168 | 1747.9175 | 1.241 |
| 2 | 3 | 1072 | 1747.9175 | 0.613 |
| 3 | 1 | 2241 | 1862.25 | 1.203 |
| 3 | 2 | 2306 | 1862.25 | 1.238 |
| 3 | 3 | 1105 | 1862.25 | 0.593 |
| 4 | 1 | 2280 | 1862.25 | 1.224 |
| 4 | 2 | 2408 | 1862.25 | 1.292 |
| 4 | 3 | 1120 | 1862.25 | 0.601 |

**5. Calculate the Seasonal Indices**

* **Calculate the average RMA for each season:**
    * Season 1: (1.062 + 1.141 + 1.203 + 1.224) / 4 = 1.1575
    * Season 2: (1.151 + 1.241 + 1.238 + 1.292) / 4 = 1.2305
    * Season 3: (0.563 + 0.613 + 0.593 + 0.601) / 4 = 0.5925

* **Adjust the seasonal indices to sum to 3 (since there are 3 seasons):**
    * Season 1: (1.1575 / 1.1575 + 1.2305 + 0.5925) * 3 = 1.101
    * Season 2: (1.2305 / 1.1575 + 1.2305 + 0.5925) * 3 = 1.168
    * Season 3: (0.5925 / 1.1575 + 1.2305 + 0.5925) * 3 = 0.565

**6. Deseasonalize the Data**

* Divide the actual sales for each period by the corresponding seasonal index.

| Year | Season | Sales | Seasonal Index | Deseasonalized Sales |
|---|---|---|---|---|
| 1 | 1 | 1856 | 1.101 | 1685.68 |
| 1 | 2 | 2012 | 1.168 | 1720.86 |
| 1 | 3 | 985 | 0.565 | 1743.36 |
| 2 | 1 | 1995 | 1.101 | 1811.90 |
| 2 | 2 | 2168 | 1.168 | 1855.17 |
| 2 | 3 | 1072 | 0.565 | 1898.23 |
| 3 | 1 | 2241 | 1.101 | 2035.26 |
| 3 | 2 | 2306 | 1.168 | 1972.22 |
| 3 | 3 | 1105 | 0.565 | 1955.31 |
| 4 | 1 | 2280 | 1.101 | 2070.91 |
| 4 | 2 | 2408 | 1.168 | 2060.87 |
| 4 | 3 | 1120 | 0.565 | 1982.30 |

**7. Trend Analysis**

* **Plot the deseasonalized sales data.**
* **Visually inspect the plot to identify a trend (linear, quadratic, etc.).**
* **Fit a trend line (e.g., linear regression) to the deseasonalized data.**

**8. Forecasting**

* **Use the trend line to forecast future deseasonalized sales.**
* **Multiply the forecasted deseasonalized sales by the appropriate seasonal index to obtain the final forecast.**

**Note:** This analysis provides a basic framework. More sophisticated methods can be used for trend identification and forecasting, such as exponential smoothing or ARIMA models.

This analysis provides a framework for understanding the trend and seasonality in the sales data. You can further refine the analysis by:

* **Visualizing the data:** Create plots of the original data, seasonal indices, and deseasonalized data to better understand the patterns.
* **Considering external factors:** Investigate potential external factors that may influence sales (e.g., economic conditions, marketing campaigns).
* **Using more advanced forecasting methods:** Explore more sophisticated techniques like exponential smoothing or ARIMA models for more accurate forecasts.