The yearly output (in thousand units) of a factory is given below.
| Year | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 |
| Output (in thousand units) | 12 | 18 | 15 | 15 | 21 | 18 | 18 | 24 | 21 |
The 3-year moving averages of the output are
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 15, 16, 17, 18, 19, 20, 21
Nine years give 9 − 3 + 1 = 7 moving averages, for the years 2017 to 2023. Each is the mean of three consecutive years, placed against the middle year:
\( \displaystyle 2017: \frac{12 + 18 + 15}{3} = 15 \)
\( \displaystyle 2018: \frac{18 + 15 + 15}{3} = 16 \)
\( \displaystyle 2019: \frac{15 + 15 + 21}{3} = 17 \)
\( \displaystyle 2020: \frac{15 + 21 + 18}{3} = 18 \)
\( \displaystyle 2021: \frac{21 + 18 + 18}{3} = 19 \)
\( \displaystyle 2022: \frac{18 + 18 + 24}{3} = 20 \)
\( \displaystyle 2023: \frac{18 + 24 + 21}{3} = 21 \)
The output goes up and down in a pattern that repeats every 3 years. The 3-year moving averages smooth out this pattern and leave a steady trend that rises by 1 thousand units every year.