Weighted Moving Average Formula & 3 year Weighted Moving Average Example

Formula

Examples
1) 3 year Weighted Moving Average
year 1 2 3 4 5 6 7 8 9 10 11 12
Sales 5.2 4.9 5.5 4.9 5.2 5.7 5.4 5.8 5.9 6 5.2 4.8
Calculate 3 year Weighted Moving Average with weight=1,2,1

Solution:
The value of table for

x $x$ and

y $y$

x	1	2	3	4	5	6	7	8	9	10	11	12
y	5.2	4.9	5.5	4.9	5.2	5.7	5.4	5.8	5.9	6	5.2	4.8

The weights of the 3 years are respectively 1,2,1 and their sum is 4
Calculation of 3 year moving averages of the data

(1) year	(2) Sales	(3) 3 year weighted moving total	(4) 3 year weighted moving average (3)÷4 $(3)-:4$
1	5.2
2	4.9	1×5.2+2×4.9+1×5.5=20.5 $1xx5.2+2xx4.9+1xx5.5=20.5$	20.5÷4=5.125 $20.5-:4=5.125$
3	5.5	1×4.9+2×5.5+1×4.9=20.8 $1xx4.9+2xx5.5+1xx4.9=20.8$	20.8÷4=5.2 $20.8-:4=5.2$
4	4.9	1×5.5+2×4.9+1×5.2=20.5 $1xx5.5+2xx4.9+1xx5.2=20.5$	20.5÷4=5.125 $20.5-:4=5.125$
5	5.2	1×4.9+2×5.2+1×5.7=21 $1xx4.9+2xx5.2+1xx5.7=21$	21÷4=5.25 $21-:4=5.25$
6	5.7	1×5.2+2×5.7+1×5.4=22 $1xx5.2+2xx5.7+1xx5.4=22$	22÷4=5.5 $22-:4=5.5$
7	5.4	1×5.7+2×5.4+1×5.8=22.3 $1xx5.7+2xx5.4+1xx5.8=22.3$	22.3÷4=5.575 $22.3-:4=5.575$
8	5.8	1×5.4+2×5.8+1×5.9=22.9 $1xx5.4+2xx5.8+1xx5.9=22.9$	22.9÷4=5.725 $22.9-:4=5.725$
9	5.9	1×5.8+2×5.9+1×6=23.6 $1xx5.8+2xx5.9+1xx6=23.6$	23.6÷4=5.9 $23.6-:4=5.9$
10	6	1×5.9+2×6+1×5.2=23.1 $1xx5.9+2xx6+1xx5.2=23.1$	23.1÷4=5.775 $23.1-:4=5.775$
11	5.2	1×6+2×5.2+1×4.8=21.2 $1xx6+2xx5.2+1xx4.8=21.2$	21.2÷4=5.3 $21.2-:4=5.3$
12	4.8

2) 3 year Weighted Moving Average
year 1 2 3 4 5 6 7 8 9 10
Sales 30 25 35 25 20 30 35 40 30 45
Calculate 3 year Weighted Moving Average with weight=1,2,1

Solution:
The value of table for

x $x$ and

y $y$

x	1	2	3	4	5	6	7	8	9	10
y	30	25	35	25	20	30	35	40	30	45

The weights of the 3 years are respectively 1,2,1 and their sum is 4
Calculation of 3 year moving averages of the data

(1) year	(2) Sales	(3) 3 year weighted moving total	(4) 3 year weighted moving average (3)÷4 $(3)-:4$
1	30
2	25	1×30+2×25+1×35=115 $1xx30+2xx25+1xx35=115$	115÷4=28.75 $115-:4=28.75$
3	35	1×25+2×35+1×25=120 $1xx25+2xx35+1xx25=120$	120÷4=30 $120-:4=30$
4	25	1×35+2×25+1×20=105 $1xx35+2xx25+1xx20=105$	105÷4=26.25 $105-:4=26.25$
5	20	1×25+2×20+1×30=95 $1xx25+2xx20+1xx30=95$	95÷4=23.75 $95-:4=23.75$
6	30	1×20+2×30+1×35=115 $1xx20+2xx30+1xx35=115$	115÷4=28.75 $115-:4=28.75$
7	35	1×30+2×35+1×40=140 $1xx30+2xx35+1xx40=140$	140÷4=35 $140-:4=35$
8	40	1×35+2×40+1×30=145 $1xx35+2xx40+1xx30=145$	145÷4=36.25 $145-:4=36.25$
9	30	1×40+2×30+1×45=145 $1xx40+2xx30+1xx45=145$	145÷4=36.25 $145-:4=36.25$
10	45

This material is intended as a summary. Use your textbook for detail explanation.
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1. Formula & 3 year Weighted Moving Average Example