Question

(b) 

For the following data, verify that the 5 year weighted moving average with weights 1, 2, 

2, 2, 1 respectively is equivalent to 4 year centred moving average:  

Year 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 

Sales (K) 5 3 7 6 4 8 9 10 8 9 9 

Answer 1

$\text{The centered moving average is given by}\\ \frac{(k_8 + k_9 + k_{10} + k_{11})}{4}\\ = \frac{(10 + 8 + 9 + 9)}{4} = 9\\ \text{The weighted moving average is given by}\\ \frac{1}{8}.9+\frac{2}{8}.10+\frac{2}{8}.8+\frac{2}{8}.9+\frac{1}{8}.9=9\\ \text{Hence they are equivalent}$