If three year moving averages for five data items given by 16, 18, 20, 10, 21 are x, y and z respectively, then:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(y \lt z \lt x\)
Each three-year moving average is the mean of three consecutive items, the window moving on by one item each time:
\( \displaystyle x = \frac{16 + 18 + 20}{3} = \frac{54}{3} = 18 \)
\( \displaystyle y = \frac{18 + 20 + 10}{3} = \frac{48}{3} = 16 \)
\( \displaystyle z = \frac{20 + 10 + 21}{3} = \frac{51}{3} = 17 \)
Since \(16 \lt 17 \lt 18\), we get \(y \lt z \lt x\).