Moving averages are widely used in time series analysis to smooth out short-term fluctuations and highlight longer-term trends or cycles. In this case, the three-year moving average takes the average of three consecutive data points. It’s useful in predicting future values based on past trends. Always ensure that you're correctly calculating the average by considering the correct number of data points in each set for moving averages.
The three-year moving average is computed by averaging three sequential data points.
Calculation of the first moving average:
\( \text{Average} = \frac{12 + 15 + 18}{3} = \frac{45}{3} = 15. \)
Calculation of the second moving average:
\( \text{Average} = \frac{15 + 18 + 24}{3} = \frac{57}{3} = 19. \)
Calculation of the third moving average:
\( \text{Average} = \frac{18 + 24 + 36}{3} = \frac{78}{3} = 26. \)
The resulting three-year moving averages are 15, 19, and 26.
| \(\text{Length (in mm)}\) | 70-80 | 80-90 | 90-100 | 100-110 | 110-120 | 120-130 | 130-140 |
|---|---|---|---|---|---|---|---|
| \(\text{Number of leaves}\) | 3 | 5 | 9 | 12 | 5 | 4 | 2 |