From the following data on the production of a factory (in '000 units) for 2016-2022, calculate the trend values by the method of 3-yearly moving averages.
| Year | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 |
|---|---|---|---|---|---|---|---|
| Production | 20 | 22 | 27 | 25 | 31 | 29 | 36 |
Step 1 — form 3-yearly moving totals (each total covers a year, the year before it, and the year after it):
| Year | Production | 3-yr Moving Total | 3-yr Moving Average (Trend) |
|---|---|---|---|
| 2016 | 20 | — | — |
| 2017 | 22 | 20+22+27 = 69 | 69/3 = 23.00 |
| 2018 | 27 | 22+27+25 = 74 | 74/3 = 24.67 |
| 2019 | 25 | 27+25+31 = 83 | 83/3 = 27.67 |
| 2020 | 31 | 25+31+29 = 85 | 85/3 = 28.33 |
| 2021 | 29 | 31+29+36 = 96 | 96/3 = 32.00 |
| 2022 | 36 | — | — |
Step 2 — independent check. Re-adding each triplet directly from the original data confirms the totals: , , , , — all match, so the trend values above are confirmed correct.
Note that no trend value can be computed for 2016 (no preceding year available) or 2022 (no following year available) — this is an inherent limitation of the moving average method, not a computational gap.
Trend values ('000 units): 2017 = 23.00, 2018 = 24.67, 2019 = 27.67, 2020 = 28.33, 2021 = 32.00; no trend value exists for 2016 or 2022.
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