Subjects statistics

Moving Average 927B7A

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1. **Stating the problem:** We are given yearly data from 2025 to 2031 and asked to calculate the moving average for years 2028 to 2031 using the 3-year moving average method. 2. **Formula used:** The 3-year moving average for year $t$ is calculated as: $$\text{Moving Average}_t = \frac{x_{t-2} + x_{t-1} + x_t}{3}$$ where $x_t$ is the data value at year $t$. 3. **Calculations:** - For 2028: $$\frac{10 + 12 + 18}{3} = \frac{40}{3} = 13.33$$ - For 2029: $$\frac{12 + 18 + 16}{3} = \frac{46}{3} = 15.33$$ - For 2030: $$\frac{18 + 16 + 12}{3} = \frac{46}{3} = 15.33$$ - For 2031: $$\frac{16 + 12 + 20}{3} = \frac{48}{3} = 16.00$$ 4. **Explanation:** The moving average smooths out short-term fluctuations by averaging data points over a fixed period (3 years here). This helps identify trends more clearly. 5. **Summary:** The moving averages for years 2028 to 2031 are 13.33, 15.33, 15.33, and 16.00 respectively.