For the given 9 values, 4,5,5,6,7,8,9,8,10, the three years moving av…

The correct answer is Option (3) → 4.66, 5.33, 6, 7, 8, 8.33, 9

A three-year moving average is the mean of each group of three consecutive values, taken in order: values 1–3, then 2–4, then 3–5, and so on. Nine values give 9 − 3 + 1 = 7 averages.

    \( \displaystyle \frac{4+5+5}{3}=\frac{14}{3}=4.66\ldots \)

    \( \displaystyle \frac{5+5+6}{3}=\frac{16}{3}=5.33\ldots \)

    \( \displaystyle \frac{5+6+7}{3}=6 \)

    \( \displaystyle \frac{6+7+8}{3}=7 \)

    \( \displaystyle \frac{7+8+9}{3}=8 \)

    \( \displaystyle \frac{8+9+8}{3}=\frac{25}{3}=8.33\ldots \)

    \( \displaystyle \frac{9+8+10}{3}=9 \)

So the moving averages, in order, are 4.66, 5.33, 6, 7, 8, 8.33, 9 (the options cut the recurring decimals off after two decimal places).