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Worked Examples · Example 5
Q.

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.

Year20152016201720182019202020212022
Sales5054496160686572
Gujarat GsebTextbookSubjectiveImportance★★★★★
15% · 6/41 Questions
✓ Free question

Step 1 — 4-yearly moving totals and averages (each average falls between the 2nd and 3rd year of its group of four):

Years coveredMoving TotalMoving AverageFalls between
2015-201850+54+49+61 = 214214/4 = 53.502016 & 2017
2016-201954+49+61+60 = 224224/4 = 56.002017 & 2018
2017-202049+61+60+68 = 238238/4 = 59.502018 & 2019
2018-202161+60+68+65 = 254254/4 = 63.502019 & 2020
2019-202260+68+65+72 = 265265/4 = 66.252020 & 2021

Step 2 — centring (2-yearly moving average of the above averages), to place each trend value onto an actual year:

YearCentring calculationCentred Trend Value
2017(53.50+56.00)/254.75
2018(56.00+59.50)/257.75
2019(59.50+63.50)/261.50
2020(63.50+66.25)/264.875

Independent check. Recomputing each 4-year total directly from the original series — e.g. 50+54+49+61=21450+54+49+61=214 and 54+49+61+60=22454+49+61+60=224 — 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.

✓Final answer

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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