From the following data on a company's sales (Rs lakh) for 2015-2022, compute the trend values by the method of 4-yearly moving averages.
| Year | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 |
|---|---|---|---|---|---|---|---|---|
| Sales | 50 | 54 | 49 | 61 | 60 | 68 | 65 | 72 |
Step 1 — 4-yearly moving totals and averages (each average falls between the 2nd and 3rd year of its group of four):
| Years covered | Moving Total | Moving Average | Falls between |
|---|---|---|---|
| 2015-2018 | 50+54+49+61 = 214 | 214/4 = 53.50 | 2016 & 2017 |
| 2016-2019 | 54+49+61+60 = 224 | 224/4 = 56.00 | 2017 & 2018 |
| 2017-2020 | 49+61+60+68 = 238 | 238/4 = 59.50 | 2018 & 2019 |
| 2018-2021 | 61+60+68+65 = 254 | 254/4 = 63.50 | 2019 & 2020 |
| 2019-2022 | 60+68+65+72 = 265 | 265/4 = 66.25 | 2020 & 2021 |
Step 2 — centring (2-yearly moving average of the above averages), to place each trend value onto an actual year:
| Year | Centring calculation | Centred Trend Value |
|---|---|---|
| 2017 | (53.50+56.00)/2 | 54.75 |
| 2018 | (56.00+59.50)/2 | 57.75 |
| 2019 | (59.50+63.50)/2 | 61.50 |
| 2020 | (63.50+66.25)/2 | 64.875 |
Independent check. Recomputing each 4-year total directly from the original series — e.g. and — reproduces the same totals, confirming the averages before centring; the centring step itself is then a simple, verifiable pairwise average.
As with the 3-yearly case, no trend value is available for 2015, 2016, 2021, or 2022 — the years lost at both ends grow with the length of the moving-average period.
Centred trend values (Rs lakh): 2017 = 54.75, 2018 = 57.75, 2019 = 61.50, 2020 = 64.875; no trend value for 2015, 2016, 2021, 2022.
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