A company's sales (₹ lakh) for the years 2015 to 2021 were as follows. Calculate the trend values by the method of 3-yearly moving averages.
| Year | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 |
|---|---|---|---|---|---|---|---|
| Sales (₹ lakh) | 12 | 15 | 21 | 24 | 27 | 33 | 36 |
Step 1 — Set up the 3-yearly moving totals. Take three consecutive years at a time, sliding forward by one year each time:
- 2016 (middle of 2015-16-17):
- 2017 (middle of 2016-17-18):
- 2018 (middle of 2017-18-19):
- 2019 (middle of 2018-19-20):
- 2020 (middle of 2019-20-21):
Step 2 — Divide each moving total by 3 to get the moving average (trend value), and place it against the middle year of its block:
| Year | Sales | 3-yearly moving total | Trend value (moving average) |
|---|---|---|---|
| 2015 | 12 | — | — |
| 2016 | 15 | 48 | |
| 2017 | 21 | 60 | |
| 2018 | 24 | 72 | |
| 2019 | 27 | 84 | |
| 2020 | 33 | 96 | |
| 2021 | 36 | — | — |
Verification: re-adding each block independently confirms the totals: ✓, ✓, ✓, ✓, ✓; dividing each by 3 gives the same trend values 16, 20, 24, 28, 32, which rise by a constant 4 each year — a smooth, believable trend compared with the more jagged original sales figures.
Trend values: 2016 = 16, 2017 = 20, 2018 = 24, 2019 = 28, 2020 = 32 (₹ lakh); 2015 and 2021 have no trend value because a full 3-year block cannot be centred on them.
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