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Worked Examples · Example 4
Q.

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.

Year2016201720182019202020212022
Production20222725312936
Gujarat GsebTextbookSubjectiveImportance★★★★★
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✓ Free question

Step 1 — form 3-yearly moving totals (each total covers a year, the year before it, and the year after it):

YearProduction3-yr Moving Total3-yr Moving Average (Trend)
201620——
20172220+22+27 = 6969/3 = 23.00
20182722+27+25 = 7474/3 = 24.67
20192527+25+31 = 8383/3 = 27.67
20203125+31+29 = 8585/3 = 28.33
20212931+29+36 = 9696/3 = 32.00
202236——

Step 2 — independent check. Re-adding each triplet directly from the original data confirms the totals: 20+22+27=6920+22+27=69, 22+27+25=7422+27+25=74, 27+25+31=8327+25+31=83, 25+31+29=8525+31+29=85, 31+29+36=9631+29+36=96 — 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.

✓Final answer

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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