Type I
				Simple aggregative Index Number
	Illustration:-
1			Commodity	Base	Current
					price
				1961	1965
				(Rs.per Ql.)	(Rs. Per Ql.)
				p0	p1
			Rice	32	50
			Wheat	25	25
			Oil(edible)	90	100
			Fish	120	140
			Potato	35	40
				302	355
			∑p0 =	302		∑p1 =	355
		Hence simple aggregative simple index number =				∑p1/∑p0*100 =	117.5
	Application :-
			Commodity	Base	Current
				price	price
		Year
				Rs.	Rs.
				p0	p1
		→
				0	0
			∑p0 =	0		∑p1 =	0
		Hence simple aggregative simple index number =				∑p1/∑p0*100 =	#DIV/0!
	Type II
			Weighted Aggregative Index Number
	2		Commodity	Base	Current
				price	price	Weight
		Year		1961	1965
				(Rs.per Ql.)	(Rs. Per Ql.)
				p0	p1	w	p0w	p1w
			Rice	32	50	8	256	400
			Wheat	25	25	6	150	150
			Oil(edible)	90	100	7	630	700
			Fish	120	140	3	360	420
			Potato	35	40	5	175	200
							1571	1870
				∑p1w =	1870	∑p0w =	1571
		Hence weighted aggregative index number   =				∑p1w/∑p0w*100 =		119.03
	Application :-
			Weighted Aggregative Index Number
			Commodity	Base	Current
				price	price	Weight
		Year		1961	1965
				(Rs.per Ql.)	(Rs. Per Ql.)
				p0	p1	w	p0w	p1w
		→					0	0
							0	0
							0	0
							0	0
							0	0
							0	0
				∑p1w =	0	∑p0w =	0
		Hence weighted aggregative index number   =				∑p1w/∑p0w*100 =		#DIV/0!
	Type III
			Classification of Index Number (Laspeyere's formula)
	3		Commodity	Base Year	Base Year	Current year
				1957	1957	1959
				Quantities	Prices	Prices
					Rs.	Rs.
				q0	p0	p1	p1q0	p0q0
			Rice	20	40	48	960	800
			Wheat	16	25	27	432	400
			Oil(edible)	8	95	105	840	760
			Fish	10	110	120	1200	1100
			Milk	6	80	100	600	480
							4032	3540
			By Laspeyre"s Formula,
			required Index Number =		∑p1q0/∑p0q0*100 =		113.9
		(If the current year quantities are used as weights, the Index Number arrived at is known as
		Paasche's Index)
	Application :-
			Classification of Index Number (Laspeyere's formula)
			Commodity	Base Year	Base Year	Current year
				1957	1957	1959
				Quantities	Prices	Prices
					Rs.	Rs.
				q0	p0	p1	p1q0	p0q0
			Rice				0	0
			Wheat				0	0
			Oil(edible)				0	0
			Fish				0	0
			Milk				0	0
							0	0
			By Laspeyre"s Formula,
			required Index Number =		∑p1q0/∑p0q0*100 =		#DIV/0!
		(If the current year quantities are used as weights, the Index Number arrived at is known as
		Paasche's Index)
	Type IV
	4	Calculate the Laspeyres' and the Paasche's Index Numbers for the following data
			Commodity	Base Year		Current Year
				Quantity	Price per lb.	Quantity	Price per lb.
			A	10.00	0.8	11	0.7
			B	8	0.85	9	0.9
			C	5	1.3	3.5	0.8
			Calculation of Laspeyres' and Paasche's Indices
		Base Year		Current Year
	Commodity
		Price	Quantity	Price	Quantity
		p0	q0	p1	q1	p0q0	p0q1	p1q0	p1q1
	A	0.8	10.00	0.7	11	8	8.8	7	7.7
	B	0.85	8	0.9	9	6.8	7.65	7.2	8.1
	C	1.3	5	0.8	5.5	6.5	7.15	4	4.4
	Total					21.3	23.6	18.2	20.2
						=∑p0q0	=∑p0q1	=∑p1q0	=∑p1q1
			Laspeyres' Index =		∑p1q0/∑p0q0*100 =		85.45
			Paasche's Index =		∑p1q1/∑p0q1*100 =		85.59
	Application :-
			Calculation of Laspeyres' and Paasche's Indices
		Base Year		Current Year
	Commodity
		Price	Quantity	Price	Quantity
		p0	q0	p1	q1	p0q0	p0q1	p1q0	p1q1
	A					0	0	0	0
	B					0	0	0	0
	C					0	0	0	0
	Total					0	0	0	0
						=∑p0q0	=∑p0q1	=∑p1q0	=∑p1q1
			Laspeyres' Index =		∑p1q0/∑p0q0*100 =		#DIV/0!
			Paasche's Index =		∑p1q1/∑p0q1*100 =		#DIV/0!
5	Type V			Calculation for Marshall Edgeworth Index
					&
				Calculation for Fisher's Ideal Index
		1970		1974
	Commodity
		Price	Quantity	Price	Quantity
		p0	q0	p1	q1	p0q0	p0q1	p1q0	p1q1
	A	2	74	3	82	148	164	222	246
	B	5	125	4	140	625	700	500	560
	C	7	40	6	33	280	231	240	198
	Total					1053	1095	962	1004
						=∑p0q0	=∑p0q1	=∑p1q0	=∑p1q1
			Marshall-Edgeworth Index =		∑p1(q0 + q1)/∑p0(q0 + q1)*100 =
			Marshall-Edgeworth Index =		91.527
			Fisher's Ideal Index =		√(∑p1q0/∑p0q0)*(∑p1q1/∑p0q1)*100
			Fisher's Ideal Index =		91.524
6				Computation of Fisher's Ideal Index
		1950		1960
	Commodity
		Price	Quantity	Price	Quantity
		p0	q0	p1	q1	p0q0	p0q1	p1q0	p1q1
	I	5	10	4	12	50	60	40	48
	II	8	6	7	7	48	56	42	49
	III	6	3	5	4	18	24	15	20
						116	140	97	117
			Fisher's Ideal Index =		√(∑p1q0/∑p0q0)*(∑p1q1/∑p0q1)*100
			Fisher's Ideal Index =		83.6
	Application :-
				Calculation for Marshall Edgeworth Index
					&
				Calculation for Fisher's Ideal Index
	Year
	Commodity
		Price	Quantity	Price	Quantity
		p0	q0	p1	q1	p0q0	p0q1	p1q0	p1q1
	A					0	0	0	0
	B					0	0	0	0
	C					0	0	0	0
	Total					0	0	0	0
						=∑p0q0	=∑p0q1	=∑p1q0	=∑p1q1
			Marshall-Edgeworth Index =		∑p1(q0 + q1)/∑p0(q0 + q1)*100
			Marshall-Edgeworth Index =		#DIV/0!
			Fisher's Ideal Index =		√(∑p1q0/∑p0q0)*(∑p1q1/∑p0q1)*100 =
			Fisher's Ideal Index =		#DIV/0!
	Application :-
				Computation of Fisher's Ideal Index
	Year	1950		1960
	Commodity
		Price	Quantity	Price	Quantity
		p0	q0	p1	q1	p0q0	p0q1	p1q0	p1q1
	I					0	0	0	0
	II					0	0	0	0
	III					0	0	0	0
						0	0	0	0
			Fisher's Ideal Index =		√(∑p1q0/∑p0q0)*(∑p1q1/∑p0q1)*100
			Fisher's Ideal Index =		#DIV/0!
7	Type VI		Calculaton of price indices by different formulae
		Base Year		Current Year
	Commodity	1970		1980
		Price	Quantity	Price	Quantity
		p0	q0	p1	q1	p0q0	p0q1	p1q0	p1q1
	A	20	8	40	6	160	120	320	240
	B	50	10	60	5	500	250	600	300
	C	40	15	50	15	600	600	750	750
	D	20	20	20	25	400	500	400	500
	Total					1660	1470	2070	1790
						=∑p0q0	=∑p0q1	=∑p1q0	=∑p1q1
			(i)	Laspeyres' Index =		∑p1q0/∑p0q0*100 =		124.70
			(ii)	Paasche's Index =		∑p1q1/∑p0q1*100 =		121.77
			(iii)	Marshall-Edgeworth Index =		∑p1(q0 + q1)/∑p0(q0 + q1)*100 =			123.32
			iv)	Fisher's Ideal Index =		√(∑p1q0/∑p0q0)*(∑p1q1/∑p0q1)*100 =			123.23
	Type VI		Calculaton of price indices by different formulae
		Base Year		Current Year
	Commodity
		Price	Quantity	Price	Quantity
		p0	q0	p1	q1	p0q0	p0q1	p1q0	p1q1
	A					0	0	0	0
	B					0	0	0	0
	C					0	0	0	0
	D					0	0	0	0
	Total					0	0	0	0
						=∑p0q0	=∑p0q1	=∑p1q0	=∑p1q1
			(i)	Laspeyres' Index =		∑p1q0/∑p0q0*100 =		#DIV/0!
			(ii)	Paasche's Index =		∑p1q1/∑p0q1*100 =		#DIV/0!
			(iii)	Marshall-Edgeworth Index =		∑p1(q0 + q1)/∑p0(q0 + q1)*100 =			#DIV/0!
			iv)	Fisher's Ideal Index =		√(∑p1q0/∑p0q0)*(∑p1q1/∑p0q1)*100 =			#DIV/0!
	Illustration:-
8	Calculate Fisher's Ideal Index using the following data and check whether it satisfies the
	"Time Reversal Test".
		Commodities	1974		1975
			Quantity	Price(Rs.)	Quantity	Price(Rs.)
		X	50	32	50	30
		Y	35	30	40	25
		Z	55	16	50	18
			Calculations for Fisher's Ideal Index
		Commodities	1974		1975
			q0	p0	q1	p1	p0q0	p0q1	p1q0	p1q1
		X	50	32	50	30	1600	1600	1500	1500
		Y	35	30	40	25	1050	1200	875	1000
		Z	55	16	50	18	880	800	990	900
							3530	3600	3365	3400
			Fisher's Ideal Index =		√(∑p1q0/∑p0q0)*(∑p1q1/∑p0q1)*100 =			94.88
			Fisher's Price Index (P01)  =		94.88
			AgainP10 =	√[(∑p1q0/∑p1q1)*(∑p0q0/∑p1q0)]
			P10 =	0.99	(Omitting the factor 100)
			P01 =	0.95	(Omitting the factor 100)
			P01 *P10 =	0.93
			P01 *P10 =	1
		OR	P01 *P10 =	1
			This shows that Fisher's Index satisfies Time Reversal Test.
	Application:-
	Calculate Fisher's Ideal Index using the following data and check whether it satisfies the
	"Time Reversal Test".
		Commodities
			Quantity	Price(Rs.)	Quantity	Price(Rs.)
		X
		Y
		Z
			Calculations for Fisher's Ideal Index
		Commodities	1974		1975
			q0	p0	q1	p1	p0q0	p0q1	p1q0	p1q1
		X	0	0	0	0	0	0	0	0
		Y	0	0	0	0	0	0	0	0
		Z	0	0	0	0	0	0	0	0
							0	0	0	0
			Fisher's Ideal Index =		√(∑p1q0/∑p0q0)*(∑p1q1/∑p0q1)*100 =			#DIV/0!
			Fisher's Price Index (P01)  =		#DIV/0!
			AgainP10 =	√[(∑p1q0/∑p1q1)*(∑p0q0/∑p1q0)]
			P10 =	#DIV/0!	(Omitting the factor 100)
			P01 =	#DIV/0!	(Omitting the factor 100)
			P01 *P10 =	#DIV/0!
			P01 *P10 =	#DIV/0!
		OR	P01 *P10 =	#DIV/0!
			This shows that Fisher's Index satisfies Time Reversal Test.
9	Illustration:-
	The group indices and the corresponding weights for the working class cost of living index numbers in an
	industrial city for the years		1976	and	1980	are given below.
					Group Index
		Group		Weight	1976	1980
		Food		71	370	380
		Clothing		3	423	504
		Fuel etc.		9	469	336
		House rent		7	110	116
		Misc.		10	279	283
	Compare the cost of living indices for the two years				1976	and	1980
	If a worker was getting		300	per month in	1976	do you think that he should be givenextra
	allowance so that he can maintain his			1976	standard of living? If so,what should be the minimum
	amont of extra allowance?
				Calculation for cost of Living Index
					Group Index
		Group		Weight	1976	1980
				w	I1	I2	I1w	I2w
		Food		71	370	380	26270	26980
		Clothing		3	423	504	1269	1512
		Fuel etc.		9	469	336	4221	3024
		House rent		7	110	116	770	812
		Misc.		10	279	283	2790	2830
				100			35320	35158
			∑w =	100	∑I1w =	35320	∑I2w =	35158
			Cost of Living Index for		1976	=	∑I1w /∑w =	353.2
			Cost of Living Index for		1980	=	∑I2w/∑w =	351.58
	Since the Cost of Living Index for			1980	is slightly less than the Cost of Living Index for
	1976	the worker eed not be given  any extra allowance to maintain his					1976
	standard of living.
		The Cost of Living Index for		1980	relative to that of		1976	=	0.9954
		and to maintain the same standard of living as				1976
		the worker needs		298.62
		But he is already getting		300
	Application:-
	The group indices and the corresponding weights for the working class cost of living index numbers in an
	industrial city for the years			and		are given below.
					Group Index
		Group		Weight	0	0
		Food
		Clothing
		Fuel etc.
		House rent
		Misc.
	Compare the cost of living indices for the two years				0	and	0
	If a worker was getting			per month in	0	do you think that he should be givenextra
	allowance so that he can maintain his			0	standard of living? If so,what should be the minimum
	amont of extra allowance?
				Calculation for cost of Living Index
					Group Index
		Group		Weight	0	0
				w	I1	I2	I1w	I2w
		Food		0	0	0	0	0
		Clothing		0	0	0	0	0
		Fuel etc.		0	0	0	0	0
		House rent		0	0	0	0	0
		Misc.		0	0	0	0	0
				0			0	0
			∑w =	0	∑I1w =	0	∑I2w =	0
			Cost of Living Index for		0	=	∑I1w /∑w =	#DIV/0!
			Cost of Living Index for		0	=	∑I2w/∑w =	#DIV/0!
	Since the Cost of Living Index for			0	is slightly less than the Cost of Living Index for
	0	the worker eed not be given  any extra allowance to maintain his					0
	standard of living.
		The Cost of Living Index for		0	relative to that of		0	=	#DIV/0!
		and to maintain the same standard of living as				0
		the worker needs		#DIV/0!
		But he is already getting		0
		Note:-	If the Cost of Living Index for the present year is more than the Cost of LivingIndex
			of the compared year then the result will be different and extral allowance will have to be given accordingly.
	Illustration:-
10	Using the following data, show that Fisher's Ideal formula satisfies the Factor Reversal Test.
		Price (in /Rs.) per unit		Number of units
	Commodity	Base	Current	Base	Current
		period	period	Period	period
	A	6	10	50	56
	B	2	2	100	120
	C	4	6	60	60
	D	10	12	30	24
	E	8	12	40	36
				Calculation for Fisher's Ideal Index
		Price		Quantity
	Commodity
		Base	Currrent	Base	Current
		p0	p1	q0	q1	p0q0	p0q1	p1q0	p1q1
	A	6	10	50	56	300	336	500	560
	B	2	2	100	120	200	240	200	240
	C	4	6	60	60	240	240	360	360
	D	10	12	30	24	300	240	360	288
	E	8	12	40	36	320	288	480	432
						1360	1344	1900	1880
			Omitting the factor 100, Fisher's Price Index P01 is given by
				P01 =	√(∑p1q0/∑p0q0)*(∑p1q1/∑p0q1)
			Interchanging p and q , Fisher's Quantity Index Q01 is
				Q01 =	√(∑p0q1/∑p0q0)*(∑p1q1/∑p1q0)
				P01*Q01 =	√∑(p1q1)2/∑(p0q0)2  =		∑(p1q1)/∑(p0q0)
				∑(p1q1)/∑(p0q0) =		1.38
				P01*Q01 =	1.38
			This shows that Fisher's Ideal Index satisfies Factor Reversal Test.
	Application:-
	Using the following data, show that Fisher's Ideal formula satisfies the Factor Reversal Test.
		Price (in /Rs.) per unit		Number of units
	Commodity	Base	Current	Base	Current
		period	period	Period	period
	A
	B
	C
	D
	E
				Calculation for Fisher's Ideal Index
		Price		Quantity
	Commodity
		Base	Currrent	Base	Current
		p0	p1	q0	q1	p0q0	p0q1	p1q0	p1q1
	A	0	0	0	0	0	0	0	0
	B	0	0	0	0	0	0	0	0
	C	0	0	0	0	0	0	0	0
	D	0	0	0	0	0	0	0	0
	E	0	0	0	0	0	0	0	0
						0	0	0	0
			Omitting the factor 100, Fisher's Price Index P01 is given by
				P01 =	√(∑p1q0/∑p0q0)*(∑p1q1/∑p0q1)
			Interchanging p and q , Fisher's Quantity Index Q01 is
				Q01 =	√(∑p0q1/∑p0q0)*(∑p1q1/∑p1q0)
				P01*Q01 =	√∑(p1q1)2/∑(p0q0)2  =		∑(p1q1)/∑(p0q0)
				∑(p1q1)/∑(p0q0) =		#DIV/0!
				P01*Q01 =	#DIV/0!
			This shows that Fisher's Ideal Index satisfies Factor Reversal Test.
11	Illustration:-
	When the cost of cigarette was increased by				50	%	a smoker who maintained
	his former scale of consumption said that the rise of cigarette price had increased his cost of living by
	5	%	What per cent of his cost of living was due to buying cigarette before the change of price?
	Let his expenditure on cigarette before the change of price be Rs.					x
	Then his expenditure on cigarette after increase in price of cigarette =					x	+	50	%	of	x
				=	Rs.	1	x	-	0.5	x
			Hence increase in expenditure =			Rs.	0.5	x
	If	Rs.	y	be his former cost of livingthen his cost of living after the increase  in
	price of cigarette (other prces remaining fixed) =				y	+	5	%	of	y
	Hence increase in expenditure =			Rs.	1	y	+	0.05	y
		Hence increase in expenditure =			1.05	y	-	1	y
		Hence increase in expenditure =			0.05	y
			We have		0.5	x	=	0.05	y
					x	=	0.10	y
	Hence the required expenditure on cigarette before the change of price expressed as percentage
	of his cost of living =			x	/	y	*	100
			=	10	%
	Alternative solution:-
			Let the required percentage be			x
		Group	Weights	Percentage
				increase in
				price
			w	i	iw
		(i)Cigarette	x	50	50	*	x
		(ii) Other
		items	100-x	0	0
		Total	100	50	50
			∑w =	100	∑iw =	50
		Average percentage increase for all items =				∑w /∑iw =	50	*	x	/	100
			i.e	5	=	50	*	x	/	100
			Hence	x	=	10	%
	Application:-
	When the cost of cigarette was increased by					%	a smoker who maintained
	his former scale of consumption said that the rise of cigarette price had increased his cost of living by
		%	What per cent of his cost of living was due to buying cigarette before the chang of price?
	Let his expenditure on cigarette before the change of price be Rs.					x
	Then his expenditure on cigarette after increase in price of cigarette =					x	+	0	%	of	x
				=	Rs.	1	x	-	0	x
			Hence increase in expenditure =			Rs.	1	x
	If	Rs.	y	be his former cost of livingthen his cost of living after the increase  in
	price of cigarette (other prces remaining fixed) =				y	+	0	%	of	y
	Hence increase in expenditure =			Rs.	1	y	+	0	y
		Hence increase in expenditure =			1	y	-	1	y
		Hence increase in expenditure =			0	y
			We have		1	x	=	0	y
					x	=	0.00	y
	Hence the required expenditure on cigarette before the change of price expressed as percentage
	of his cost of living =			x	/	y	*	100
			=	0	%
	Alternative solution:-
			Let the required percentage be			x
		Group	Weights	Percentage
				increase in
				price
			w	i	iw
		(i)Cigarette	x	0	0	*	x
		(ii) Other
		items	100-x	0	0
		Total	100	0	0
			∑w =	100	∑iw =	0
		Average percentage increase for all items =				∑w /∑iw =	0	*	x	/	100
			i.e	0	=	0	*	x	/	100
			Hence	x	=	#DIV/0!	%
	From the following data of wholesale proces of a cerain commodity , consruct Index Numbers by chain base method.
	Year	1979	1980	1981	1982	1983	1984	1985	1986	1987	1988
	Price	750	500	650	600	720	700	690	750	840	800
	Year	Price	Link rlative	Chain base	Fixed base
				Index Numbers	Index Numbers
	1979	750	100	100	100
	1980	500	66.67	66.67	66.67
	1981	650	130.00	86.67	86.67
	1982	600	92.31	80.00	80.00
	1983	720	120.00	96.00	96.00
	1984	700	97.22	93.33	93.33
	1985	690	98.57	92.00	92.00
	1986	750	108.70	100.00	100.00
	1987	840	112.00	112.00	112.00
	1988	800	95.24	106.67	106.67
	Application: -
	Year	Price	Link rlative	Chain base	Fixed base
				Index Numbers	Index Numbers
			100	100	100
			#DIV/0!	#DIV/0!	#DIV/0!
			#DIV/0!	#DIV/0!	#DIV/0!
			#DIV/0!	#DIV/0!	#DIV/0!
			#DIV/0!	#DIV/0!	#DIV/0!
			#DIV/0!	#DIV/0!	#DIV/0!
			#DIV/0!	#DIV/0!	#DIV/0!
			#DIV/0!	#DIV/0!	#DIV/0!
			#DIV/0!	#DIV/0!	#DIV/0!
			#DIV/0!	#DIV/0!	#DIV/0!
							Application: -
	Construct chain index numbers from the link relatives given below:
	Year	Link Index	Chain Index				Year	Link Index	Chain Index
			Number						Number
	1984	100	100					100	100
	1985	105	105						0
	1986	95	99.75						0
	1987	115	114.71						0.00
	1988	102	117.01						0.00
		Input						Input
		Output						Output
	Construct Chain Index Numbers with 1984 prices as base from the following table giving the average wholesale prices of the
	commodities A, B and C for the year 1985 to 1988.
		Column1	Column2	Column3	Column4	Column5	Column6
				Average Wolesale Prices (in Rs.)
		Commodities	1984	1985	1986	1987	1988
		A	20	16	28	35	21			Input
		B	25	30	24	36	45
		C	20	25	30	24	30
			Computation of Chain Index
	Column1	Column2	Column3	Column4	Column5	Column6
			Relatives based on preceding year
										Output
	Commodity	1984	1985	1986	1987	1988
	A	100	80	175	125	60
	B	100	120	80	150	125
	C	100	125	120	80	125
	Total link
	Relatives	300	325	375	355	310
	Average of
	Link Relatives	100	108.33	125	118.33	103.33
	Chain Indices	100	108.33	135.42	160.24	165.58
		Column1	Column2	Column3	Column4	Column5	Column6
				Average Wolesale Prices (in Rs.)
		Commodities
		A								Input
		B
		C
			Computation of Chain Index
	Column1	Column2	Column3	Column4	Column5	Column6
			Relatives based on preceding year
										Output
	Commodity	1984	1985	1986	1987	1988
	A	100	#DIV/0!	#DIV/0!	#DIV/0!	#DIV/0!
	B	100	#DIV/0!	#DIV/0!	#DIV/0!	#DIV/0!
	C	100	#DIV/0!	#DIV/0!	#DIV/0!	#DIV/0!
	Total link
	Relatives	300	#DIV/0!	#DIV/0!	#DIV/0!	#DIV/0!
	Average of
	Link Relatives	100	#DIV/0!	#DIV/0!	#DIV/0!	#DIV/0!
	Chain Indices	100	#DIV/0!	#DIV/0!	#DIV/0!	#DIV/0!
		M.Sc. (Statistics)									1966
		University of Mysore
		C.P.S. IIPS, Bombay.									1976
		CMC, Ltd., Bangalore				Computers, Internet & Essentials					2001
	Experience:     Computer/Statistical Assistant/Statistician in C.M.A.I.,
			for Family Welfare Project, in Research & Evaluation
			Unit, Bengalore (Bangalore)
		Co-Author for about 10 Research Papers									18 Years
		1	Ex-Lecturer in Statistics in								2 Years
			Nursing College, Bengalore (Bangalore)
		2	Ex-Lecturer in Statistics & Mathematics for BBM
			Course in Garden City College, Bengalore (Bangalore)								I year
		3	Ex-Lecturer in Statistics & Mathematics in
			Anupama College, Rajajinagar, Bengalore (Bangalore)								4 years
		4	Experience in Central, State & Private Organizations								14 years