A series has the values 10, 14, 12, 18 and 20 for five years. What is the first centred 4-year moving average?

Explanation

1. 01

   The 4-year moving averages are $\frac{10 + 14 + 12 + 18}{4} = 13.5$ and $\frac{14 + 12 + 18 + 20}{4} = 16$; each falls between two years.

2. 02

   Centring averages the two: $\frac{13.5 + 16}{2} = 14.75$, placed against the third year.