Question

Use the method of monthly averages to find the monthly indices for the following data of production of a commodity for the years 2002, 2003 and 2004

2002	2003	2004
15	20	18
18	18	25
17	16	21
19	13	11
16	12	14
20	15	16
21	22	19
18	16	20
17	18	1
15	20	16
14	17	18
18	15	20

Answer 1

Computation of monthly indices for the production of a commodity using the method of monthly averages.

Months Years	Jan	Feb	Mar	Apr	May	Jun	July	Aug	Sep	Oct	Nov	Dec
2002	15	18	17	19	16	20	21	18	17	15	14	18
2003	20	1	16	13	12	15	22	16	18	20	17	15
2004	18	25	21	11	14	16	19	20	17	16	18	20
Monthly Total	53	61	54	43	42	51	62	54	52	51	49	53
Monthly Average	17.7	20.3	18	14.3	14	17	20.7	18	17.3	17	16.3	17.7
Seasonal Indices	102	116.9	103.7	82.4	80.6	97.9	119.2	103.7	99.7	97.9	93.9	102

Grand Average = `("Sum of"  12  "Monthly Averages")/12`

= `(17.6 + 20.3 + 18 + 14.3 + 14 + 17 + 20.6 + 18 + 17.3 + 17 + 16.3 + 17.6)/12`

= `208/12`

= 17.33

S.I for January = `("Monthly Average" ("for Jan"))/"Grand Average" xx 100`

= `17.6/17.33 xx 100`

= `1760/17.33`

= 17.33

 101.56

S.I for Febuary = `("Monthly Average" ("for Feb"))/"Grand Average" xx 100`

= `20.3/17.33 xx 100`

= `2030/17.33`

= 117.14

S.I for March = `("Monthly Average for March")/"Grand Average" xx 100`

= `18/17.33 xx 100`

= `1800/17.33`

= 103.86

S.I for April = `("Monthly Average for April")/"Grand Average" xx 100`

= `14.3/17.33 xx 100`

= `1430/17.3`

= 82.52

S.I for May = `("Monthly Average for May")/"Grand Average" xx 100`

= `14/17.33 xx 100`

= `1400/17.33`

= 80.78

S.I for June = `("Monthly Average for June")/"Grand Average" xx 100`

= `17/17.33 xx 100`

= `1700/17.33`

= 98.10

S.I for July = `("Monthly Average for July")/"Grand Average" xx 100`

= `20.6/17.33 xx 100`

= `2060/17.33`

= 118.87

S.I for August = `("Monthly Average for August")/"Grand Average" xx 100`

= `18/17.33 xx 100`

= `1800/17.33`

= 103.87

S.I for September = `("Monthly Average for September")/"Grand Average" xx 100`

= `17.3/17. xx 100`

= `1730/17.3`

= 100

S.I for October = `("Monthly Average for October")/"Grand Average" xx 100`

= `17/17.3 xx 100`

= `1700/17.33`

= 98.10

S.I for November = `("Monthly Average for November")/"Grand Average" xx 100`

= `16.3/17.33 xx 100`

= `1630/17.33`

= 94.06

S.I for December = `("Monthly Average for December")/"Grand Average" xx 100`

= `17.6/17.33 xx100`

= `1760/17.33`

= 101.56