The 3-year moving averages of the production (in tonnes) of a farm for the years 2021 and 2022 are 40 and 43 respectively. If the production in 2020 was 35 tonnes, then the production (in tonnes) in 2023 was
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 44
Let the productions in 2020, 2021, 2022, 2023 be \(y_{20}, y_{21}, y_{22}, y_{23}\). Each 3-year moving average is the mean of the year and its two neighbours, so the 3-year moving totals are
\(y_{20} + y_{21} + y_{22} = 3 \times 40 = 120\)
\(y_{21} + y_{22} + y_{23} = 3 \times 43 = 129\)
Subtracting the first total from the second, the common values cancel:
\(y_{23} - y_{20} = 129 - 120 = 9\)
\(y_{23} = 35 + 9 = 44\)
So the production in 2023 was 44 tonnes.