CS-08

Q. 6. The following table gives the average wholesale prices of the four grains for the years 1998 to 2001. Compute chain base index number. (Dec. 2001)

Grain	1998	1999	2000	2001
Rice	12	18	24	12
Wheat	18	36	54	24
Gram	12	36	60	24
Barley	15	21	54	33

Solution.

	Link relatives based on preceding years
Grain	1998	1999	2000	2001
Rice	100	150	133	50
Wheat	100	200	150	44
Gram	100	300	166	40
Barley	100	140	257	61
Total of link relatives	400	790	706	195
Average of Link Relative	100	197.5	176.5	48.75

Chain Base Index Number

100

197.5

348.58

169.33

Q. 7. The following table gives the average wholesale prices of the four grains for the years 1996 to 2000. Compute chain base index number. (June 2001)

Grain	1996	1997	1998	1999	2000
Wheat	100	120	115	125	150
Gram	100	95	105	115	98
Barley	100	110	105	95	120
Rice	100	115	110	120	115

Solution.

	Link relatives based on preceding years
Grain	1996	1997	1998	1999	2000
Wheat	100	120	95	108	120
Gram	100	95	110	109	85
Barley	100	110	95	90	126
Rice	100	115	95	109	95
Total of link relatives	400	440	395	416	426
Average of Link Relative	100	110	98.75	104	106.5

Chain Base Index Number

100

110

108.62

112.96

120.30

Q. 8. The following table gives the average wholesale prices of the four fruits for the years 1996 to 2000. Compute chain base index number. (Dec. 2002)

Fruit	1996	1997	1998	1999	2000
Apple	1600	1760	1440	1920	2000
Orange	3200	3520	3840	4000	4800
Banana	1920	2080	1680	2240	2400
Grapes	2400	2560	2880	2720	2880

Solution.

Link relatives based on preceding years
Fruit	1996	1997	1998	1999	2000
Apple	[(1600/1600) X 100] = 100	[(1760/1600) X 100] = 110	[(1440/1760) X 100] = 82	[(1920/1440) X 100] = 133	[(2000/1920) X 100] = 104
Orange	[(3200/3200) X 100] = 100	[(3520/3200) X 100] = 110	[(3840/3520) X 100] = 109	[(4000/3840) X 100] = 104	[(4800/4000) X 100] = 120
Banana	[(1920/1920) X 100] = 100	[(2080/1920) X 100] = 108	[(1680/2080) X 100] = 81	[(2240/1680) X 100] = 133	[(2400/2240) X 100] = 107
Grapes	[(2400/2400) X 100] = 100	[(2560/2400) X 100] = 107	[(2880/2560) X 100] = 112	[(2720/2880) X 100] = 94	[(2880/2720) X 100] = 106
Total of link relatives	400	435	384	464	437
Average of Link Relative	400/4 = 100	435/4 = 108.75	384/4 = 96	464/4 = 116	437/4 = 109.25

Chain Base Index Number

100

[(108.75 X 100)/100] = 108.75

[(96 X 108.75)/100] = 104.4

[(116 X 104.4)/100] = 121.10

[(109.25 X 121.10)/100] = 132.30

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