The yearly sales (in lakh Rs.) of a shop are given below.
| Year | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 |
| Sales (in lakh Rs.) | 20 | 26 | 22 | 28 | 32 | 30 | 36 |
The 4-year centred moving average for the year 2021 is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 27.5
A 4-year moving average has no middle year, so it falls between two years. The two 4-year moving averages on either side of 2021 are
\( \displaystyle 2019\text{ to }2022: \frac{26 + 22 + 28 + 32}{4} = \frac{108}{4} = 27 \) (between 2020 and 2021)
\( \displaystyle 2020\text{ to }2023: \frac{22 + 28 + 32 + 30}{4} = \frac{112}{4} = 28 \) (between 2021 and 2022)
Centring takes the mean of these two neighbouring averages and places it against 2021:
\( \displaystyle \frac{27 + 28}{2} = 27.5 \)
Why the other options are incorrect
Option (2) 27 — Incorrect. It is the 4-year moving average lying between 2020 and 2021, before centring.
Option (3) 28 — Incorrect. It is the 4-year moving average lying between 2021 and 2022, before centring.
Option (4) 29.75 — Incorrect. It is the centred moving average for 2022, the mean of 28 and 31.5.