Method of Moving Averages
Time Series — Chapter 6, GSEB Class 12 Statistics
What is a Moving Average?
A moving average smooths out short-term fluctuations to reveal the underlying trend. It takes the average of successive groups of data points.
Odd period (3, 5): MA placed on the middle row. Loses (period−1)/2 points at each end.
Even period (4): 4-year totals placed between rows, centered by averaging two consecutive totals.
Even period (4): 4-year totals placed between rows, centered by averaging two consecutive totals.
3-Year Moving Average
3-year MA placed on the middle row. First year and last year have no MA.
| Year | Sales | Total of 3 values | 3-year MA |
|---|---|---|---|
| 2018 | 12 | ||
| 2019 | 15 | 45 | 15 |
| 2020 | 18 | 55 | 18.33 |
| 2021 | 22 | 60 | 20 |
| 2022 | 20 | 67 | 22.33 |
| 2023 | 25 | 73 | 24.33 |
| 2024 | 28 | 83 | 27.67 |
| 2025 | 30 | 85 | 28.33 |
| 2026 | 27 | 89 | 29.67 |
| 2027 | 32 | 94 | 31.33 |
| 2028 | 35 | 105 | 35 |
| 2029 | 38 |
5-Year Moving Average
5-year MA placed on the middle row. First 2 and last 2 years have no MA.
| Year | Sales | Total of 5 values | 5-year MA |
|---|---|---|---|
| 2018 | 12 | ||
| 2019 | 15 | ||
| 2020 | 18 | 87 | 17.40 |
| 2021 | 22 | 100 | 20 |
| 2022 | 20 | 113 | 22.60 |
| 2023 | 25 | 125 | 25 |
| 2024 | 28 | 130 | 26 |
| 2025 | 30 | 142 | 28.40 |
| 2026 | 27 | 152 | 30.40 |
| 2027 | 32 | 162 | 32.40 |
| 2028 | 35 | ||
| 2029 | 38 |
4-Year Moving Average (Centered)
Total of 4 placed between the 2nd and 3rd values of its group. Total of 2 placed between two totals of 4, and the 4-year MA sits next to it on the same row.
| Year | Sales | Total of 4 values | Total of 2 values | 4-year MA |
|---|---|---|---|---|
| 2018 | 12 | |||
| 2019 | 15 | |||
| 67 | ||||
| 2020 | 18 | 142 | 17.75 | |
| 75 | ||||
| 2021 | 22 | 160 | 20 | |
| 85 | ||||
| 2022 | 20 | 180 | 22.50 | |
| 95 | ||||
| 2023 | 25 | 198 | 24.75 | |
| 103 | ||||
| 2024 | 28 | 213 | 26.63 | |
| 110 | ||||
| 2025 | 30 | 227 | 28.38 | |
| 117 | ||||
| 2026 | 27 | 241 | 30.13 | |
| 124 | ||||
| 2027 | 32 | 256 | 32 | |
| 132 | ||||
| 2028 | 35 | |||
| 2029 | 38 |
Pattern: total of 4 between the 2nd and 3rd values → two consecutive totals added (total of 2) → divided by 8 = 4-year MA next to it.
Merits and Limitations
Merits
- ✓ Simple to compute and understand
- ✓ Effectively removes short-term noise
- ✓ Reveals the underlying trend clearly
Limitations
- ✗ Loses data points at both ends
- ✗ Cannot forecast future values
- ✗ Larger period = smoother but loses more data
Key Takeaways
Key Takeaways
- 3-year MA: total of 3 consecutive values, MA on the middle row. Loses 1 point at each end.
- 5-year MA: total of 5 consecutive values, MA on the middle row. Loses 2 points at each end.
- 4-year MA: 4-year totals placed between rows; centered by averaging two consecutive totals; MA = centered sum / 8.
- Odd period: centered directly. Even period: needs centering.
- Larger period = smoother trend but loses more data points.