Skip to content
Worked Examples · Example 1
Q.

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.

Year2015201620172018201920202021
Sales (₹ lakh)12152124273336
Tamil Nadu DgeTextbookSubjectiveImportance★★★★★
23% · 9/39 Questions
✓ Free question

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): 12+15+21=4812+15+21 = 48
  • 2017 (middle of 2016-17-18): 15+21+24=6015+21+24 = 60
  • 2018 (middle of 2017-18-19): 21+24+27=7221+24+27 = 72
  • 2019 (middle of 2018-19-20): 24+27+33=8424+27+33 = 84
  • 2020 (middle of 2019-20-21): 27+33+36=9627+33+36 = 96

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:

YearSales3-yearly moving totalTrend value (moving average)
201512——
2016154848/3=1648/3 = 16
2017216060/3=2060/3 = 20
2018247272/3=2472/3 = 24
2019278484/3=2884/3 = 28
2020339696/3=3296/3 = 32
202136——

Verification: re-adding each block independently confirms the totals: 12+15+21=4812+15+21=48 ✓, 15+21+24=6015+21+24=60 ✓, 21+24+27=7221+24+27=72 ✓, 24+27+33=8424+27+33=84 ✓, 27+33+36=9627+33+36=96 ✓; 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.

✓Final answer

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.

Unlock everything free for 14 days

  • Full step-by-step solutions
  • Concept-first explanations
  • Methods, shortcuts & mistakes
  • PYQ mapping + timed mock tests

Full access for 14 days. No credit card required.