Index Numbers | Business Statistics MGT 202

This unit covers the meaning and types of index numbers, unweighted and weighted methods of construction (Laspeyres', Paasche's and Fisher's indices), quantity and value indices, the time reversal and factor reversal tests, the cost of living index and real wages. Worked examples follow, and board exam questions are listed at the end by exam year, with marks in brackets.

Index Numbers: Meaning and Types

An index number is a statistical device designed to measure the relative change in the level of a phenomenon with respect to time, geographical location or other characteristics such as income, profession, etc.

Types of index number:

Price index number
Quantity index number
Value index number

Notation

$p_0$ = price in the base year; $p_1$ = price in the current year
$q_0$ = quantity in the base year; $q_1$ = quantity in the current year
$P_{01}$ = price index number of the current year '1' with respect to the base year '0'

Methods of Constructing Index Numbers

Unweighted indices	Weighted indices
Simple aggregative index	Weighted aggregative index (Laspeyres', Paasche's, Fisher's)
Simple average of price relatives	Weighted average of price relatives

Unweighted Indices

Simple Aggregative Index

$$P_{01} = \frac{\sum p_1}{\sum p_0} \times 100$$

Simple Average of Price Relatives

$$\begin{aligned} P_{01}\ (\text{A.M.}) &= \frac{\sum P}{n} \\ P_{01}\ (\text{G.M.}) &= \text{antilog}\left[\frac{\sum \log P}{n}\right] \end{aligned}$$

where $P = \dfrac{p_1}{p_0} \times 100$ is the price relative of each item and $n$ is the number of items.

Weighted Indices

Weighted Aggregative Method

$$\begin{aligned} \text{Laspeyres':}\quad P_{01}(L) &= \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100 \\ \text{Paasche's:}\quad P_{01}(P) &= \frac{\sum p_1 q_1}{\sum p_0 q_1} \times 100 \\ \text{Fisher's:}\quad P_{01}(F) &= \sqrt{P_{01}(L) \times P_{01}(P)} = \sqrt{\frac{\sum p_1 q_0}{\sum p_0 q_0} \times \frac{\sum p_1 q_1}{\sum p_0 q_1}} \times 100 \end{aligned}$$

Why Fisher's Index Is Called the “Ideal” Index

It is based on the geometric mean, which is the best average for constructing index numbers.
It takes into account both current year and base year prices and quantities.
It satisfies both the time reversal test and the factor reversal test.
It has no bias in any direction.

Comparison of Laspeyres', Paasche's and Fisher's Indices

Feature	Laspeyres'	Paasche's	Fisher's
Weight used	Base year quantity $q_0$ only	Current year quantity $q_1$ only	Both base year and current year quantities
Time reversal test	Not satisfied	Not satisfied	Satisfied
Factor reversal test	Not satisfied	Not satisfied	Satisfied

Weighted Average of Price Relatives

$$\begin{aligned} P_{01}\ (\text{A.M.}) &= \frac{\sum PW}{\sum W} \\ P_{01}\ (\text{G.M.}) &= \text{antilog}\left[\frac{\sum W \log P}{\sum W}\right] \end{aligned}$$

where $P = \dfrac{p_1}{p_0} \times 100$ is the price relative and $W = p_0 q_0$ is the weight (base year value).

Quantity and Value Index Numbers

$$\begin{aligned} Q_{01}\ (\text{simple}) &= \frac{\sum q_1}{\sum q_0} \times 100 \\ Q_{01}(L) &= \frac{\sum p_0 q_1}{\sum p_0 q_0} \times 100 \\ Q_{01}(P) &= \frac{\sum p_1 q_1}{\sum p_1 q_0} \times 100 \\ Q_{01}(F) &= \sqrt{\frac{\sum p_0 q_1}{\sum p_0 q_0} \times \frac{\sum p_1 q_1}{\sum p_1 q_0}} \times 100 \\ V_{01} &= \frac{\sum p_1 q_1}{\sum p_0 q_0} \end{aligned}$$

Tests of Consistency of Index Number Formulae

Two tests are used to check the adequacy of an index number formula: the time reversal test and the factor reversal test. The indices are used as ratios (without the factor 100) in both tests.

Time Reversal Test

A formula satisfies the time reversal test if the index for the current year on the base year, multiplied by the index for the base year on the current year, equals 1:

$$\begin{aligned} P_{01} \times P_{10} &= 1 \\ P_{10}(L) &= \frac{\sum p_0 q_1}{\sum p_1 q_1}, \qquad P_{10}(P) = \frac{\sum p_0 q_0}{\sum p_1 q_0} \\ P_{01}(F) \times P_{10}(F) &= \sqrt{\frac{\sum p_1 q_0}{\sum p_0 q_0} \times \frac{\sum p_1 q_1}{\sum p_0 q_1}} \times \sqrt{\frac{\sum p_0 q_1}{\sum p_1 q_1} \times \frac{\sum p_0 q_0}{\sum p_1 q_0}} = \sqrt{1} = 1 \end{aligned}$$

Hence Fisher's index satisfies the time reversal test; Laspeyres' and Paasche's indices do not.

Factor Reversal Test

A formula satisfies the factor reversal test if the price index multiplied by the corresponding quantity index (obtained by interchanging $p$ and $q$) equals the value index:

$$\begin{aligned} P_{01} \times Q_{01} &= V_{01} = \frac{\sum p_1 q_1}{\sum p_0 q_0} \\ P_{01}(F) \times Q_{01}(F) &= \sqrt{\frac{\sum p_1 q_0}{\sum p_0 q_0} \times \frac{\sum p_1 q_1}{\sum p_0 q_1} \times \frac{\sum p_0 q_1}{\sum p_0 q_0} \times \frac{\sum p_1 q_1}{\sum p_1 q_0}} \\ &= \sqrt{\frac{(\sum p_1 q_1)^2}{(\sum p_0 q_0)^2}} = \frac{\sum p_1 q_1}{\sum p_0 q_0} = V_{01} \end{aligned}$$

Hence Fisher's index satisfies the factor reversal test; Laspeyres' and Paasche's indices do not.

Cost of Living Index and Real Wages

The cost of living index (COLI), also called the consumer price index number, can be constructed by two methods.

Aggregate Expenditure Method

$$\text{COLI} = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100 \quad (\text{Laspeyres' index})$$

Family Budget Method

$$\text{COLI} = \frac{\sum PW}{\sum W} \quad \text{or} \quad \frac{\sum WI}{\sum W}$$

where $P = \dfrac{p_1}{p_0} \times 100$ is the price relative, $W = p_0 q_0$ (or the percentage of expenditure) is the weight, and $I$ is the group index.

Adjusting Salary to the Cost of Living

If the COLI rises from 100 to a value $C$, the cost of living has increased by $(C - 100)$%. To maintain the same standard of living, the salary must increase in the same ratio:

$$\text{Required salary} = \text{Base salary} + \frac{C - 100}{100} \times \text{Base salary} = \text{Base salary} \times \frac{C}{100}$$

Real Wage and Real Wage Index

$$\begin{aligned} \text{Real wage} &= \frac{\text{Money wage}}{\text{Price index}} \times 100 \\ \text{Real wage index} &= \frac{\text{Real wage for current year}}{\text{Real wage for base year}} \times 100 \end{aligned}$$

Worked Examples

Example 1: Simple Aggregative Price Index

Find the simple aggregative price index for 2021 (base 2020).

Commodity	A	B	C	D	E	Total
Price in 2020 $(p_0)$	10	20	18	15	12	75
Price in 2021 $(p_1)$	15	22	20	22	18	97

$$P_{01} = \frac{\sum p_1}{\sum p_0} \times 100 = \frac{97}{75} \times 100 = 129.33$$

Example 2: Price Index with a Fixed Base Year

Taking 2055 (price Rs. 650) as the base year, each year's index is $\dfrac{p_t}{650} \times 100$:

Year	2052	2053	2054	2055	2056	2057	2058	2059	2060	2061
Price (Rs.)	500	600	620	650	700	780	820	840	880	900
Index	76.92	92.31	95.38	100	107.69	120	126.15	129.23	135.38	138.46

Example 3: Laspeyres', Paasche's and Fisher's Price Indices

Commodity	$p_0$ (2014)	$q_0$	$p_1$ (2015)	$q_1$	$p_0q_0$	$p_1q_0$	$p_0q_1$	$p_1q_1$
A	10	100	20	120	1000	2000	1200	2400
B	11	150	25	180	1650	3750	1980	4500
C	12	180	30	210	2160	5400	2520	6300
D	14	200	40	250	2800	8000	3500	10000
Total					7610	19150	9200	23200

$$\begin{aligned} P_{01}(L) &= \frac{19150}{7610} \times 100 = 251.64 \\ P_{01}(P) &= \frac{23200}{9200} \times 100 = 252.17 \\ P_{01}(F) &= \sqrt{\frac{19150}{7610} \times \frac{23200}{9200}} \times 100 = 251.91 \end{aligned}$$

Example 4: Fisher's Index from Prices and Expenditure

Since expenditure = price × quantity, the quantities are found as $q = \text{expenditure} / \text{price}$.

Article	$p_0$	Exp. $p_0q_0$	$p_1$	Exp. $p_1q_1$	$q_0$	$q_1$	$p_1q_0$	$p_0q_1$
I	5	50	4	48	10	12	40	60
II	8	48	7	49	6	7	42	56
III	6	18	5	20	3	4	15	24
Total		116		117			97	140

$$P_{01}(F) = \sqrt{\frac{97}{116} \times \frac{117}{140}} \times 100 = 83.60$$

Example 5: Fisher's Index Satisfies Both Tests

Commodity	$p_0$	$p_0q_0$	$p_1$	$p_1q_1$	$q_0$	$q_1$	$p_0q_1$	$p_1q_0$
W	4	32	5	50	8	10	40	40
X	5	50	6	72	10	12	60	60
Y	3	18	4	28	6	7	21	24
Z	8	40	10	40	5	4	32	50
Total		140		190			153	174

$$\begin{aligned} P_{01}(F) &= \sqrt{\frac{174}{140} \times \frac{190}{153}} \times 100 = 124.23 \\ P_{01}(F) \times P_{10}(F) &= \sqrt{\frac{174}{140} \times \frac{190}{153}} \times \sqrt{\frac{153}{190} \times \frac{140}{174}} = \sqrt{1} = 1 \\ Q_{01}(F) &= \sqrt{\frac{153}{140} \times \frac{190}{174}} \\ P_{01}(F) \times Q_{01}(F) &= \sqrt{\frac{174}{140} \times \frac{190}{153} \times \frac{153}{140} \times \frac{190}{174}} = \sqrt{\frac{(190)^2}{(140)^2}} = \frac{190}{140} = V_{01} \end{aligned}$$

Hence Fisher's index satisfies both the time reversal test and the factor reversal test.

Example 6: Testing Laspeyres', Paasche's and Fisher's Indices

Base year prices 2, 4, 1, 5 with expenditure 40, 16, 10, 25; current year prices 5, 8, 2, 10 with expenditure 75, 40, 24, 60 (the same data as the 2083 exam question below).

Commodity	$p_0$	$p_0q_0$	$p_1$	$p_1q_1$	$q_0$	$q_1$	$p_0q_1$	$p_1q_0$
A	2	40	5	75	20	15	30	100
B	4	16	8	40	4	5	20	32
C	1	10	2	24	10	12	12	20
D	5	25	10	60	5	6	30	50
Total		91		199			92	202

$$\begin{aligned} P_{01}(L) &= \frac{202}{91} \times 100 = 221.98 \\ P_{01}(P) &= \frac{199}{92} \times 100 = 216.30 \\ P_{01}(F) &= \sqrt{\frac{202}{91} \times \frac{199}{92}} \times 100 = 219.12 \\ V_{01} &= \frac{199}{91} = 2.187 \end{aligned}$$

Index	$P_{01} \times P_{10}$	Time reversal test	$P_{01} \times Q_{01}$	Factor reversal test
Laspeyres'	$\frac{202}{91} \times \frac{92}{199} = 1.026$	Not satisfied	$\frac{202}{91} \times \frac{92}{91} = 2.244$	Not satisfied
Paasche's	$\frac{199}{92} \times \frac{91}{202} = 0.974$	Not satisfied	$\frac{199}{92} \times \frac{199}{202} = 2.131$	Not satisfied
Fisher's	1	Satisfied	$\frac{199}{91} = 2.187$	Satisfied

Example 7: Paasche's versus Fisher's Index

Commodity	$p_0$	$q_0$	$p_1$	$q_1$	$p_0q_0$	$p_1q_1$	$p_0q_1$	$p_1q_0$
A	10	6	12	10	60	120	100	72
B	12	12	15	15	144	225	180	180
C	15	25	18	30	375	540	450	450
D	20	40	25	40	800	1000	800	1000
E	13	17	20	15	221	300	195	340
Total					1600	2185	1725	2042

$$\begin{aligned} \text{Paasche's TRT:}\quad P_{01}(P) \times P_{10}(P) &= \frac{2185}{1725} \times \frac{1600}{2042} = 0.9925 \neq 1 \\ V_{01} &= \frac{2185}{1600} = 1.3656 \\ \text{Paasche's FRT:}\quad P_{01}(P) \times Q_{01}(P) &= \frac{2185}{1725} \times \frac{2185}{2042} = 1.3554 \neq V_{01} \\ \text{Fisher's TRT:}\quad P_{01}(F) \times P_{10}(F) &= \sqrt{\frac{2042}{1600} \times \frac{2185}{1725} \times \frac{1725}{2185} \times \frac{1600}{2042}} = 1 \\ \text{Fisher's FRT:}\quad P_{01}(F) \times Q_{01}(F) &= \sqrt{\frac{2042}{1600} \times \frac{2185}{1725} \times \frac{1725}{1600} \times \frac{2185}{2042}} = \frac{2185}{1600} = V_{01} \end{aligned}$$

Paasche's index fails both tests, while Fisher's index satisfies both.

Example 8: Cost of Living Index by the Family Budget Method

Expenses	Weight $W$ (%)	$p_0$	$p_1$	$P = \frac{p_1}{p_0} \times 100$	$PW$
Food	35	150	174	116	4060
Rent	15	50	60	120	1800
Clothing	20	100	125	125	2500
Fuel	10	20	25	125	1250
Miscellaneous	20	60	90	150	3000
Total	100				12610

$$\begin{aligned} \text{COLI} &= \frac{\sum PW}{\sum W} = \frac{12610}{100} = 126.10 \\ \text{Required salary} &= 20{,}000 + 26.10\% \text{ of } 20{,}000 = 20{,}000 + 5{,}220 = \text{Rs. } 25{,}220 \end{aligned}$$

The cost of living has increased by 26.10% (126.10 − 100) compared with the base period, so a salary of Rs. 20,000 must rise to Rs. 25,220 to maintain the same standard of living.

Example 9: Cost of Living Index by the Aggregate Expenditure Method

Product	$p_0$ (2008)	$q_0$	$p_1$ (2010)	$q_1$	$p_0q_0$	$p_1q_1$	$p_0q_1$	$p_1q_0$
X	4	50	10	40	200	400	160	500
Y	3	10	8	8	30	64	24	80
Z	2	5	4	4	10	16	8	20
Total					240	480	192	600

Since both base year and current year prices and quantities are given, Fisher's index is the suitable price index for these data.

$$\begin{aligned} P_{01}(F) &= \sqrt{\frac{600}{240} \times \frac{480}{192}} \times 100 = 250 \\ \text{COLI} &= \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100 = \frac{600}{240} \times 100 = 250 \\ \text{Income in 2010} &= 10{,}000 + 150\% \text{ of } 10{,}000 = \text{Rs. } 25{,}000 \end{aligned}$$

The cost of living in 2010 has increased by 150% (250 − 100) compared with 2008, so an income of Rs. 10,000 in 2008 must become Rs. 25,000 in 2010.

Example 10: COLI from Expenditure Shares and Price Relatives

Item	A	B	C	D	E	Total
% of expenditure $(W)$	25	35	15	10	15	100
Price relative $(P)$	125	140	160	130	190
$PW$	3125	4900	2400	1300	2850	14575

$$\text{COLI} = \frac{\sum PW}{\sum W} = \frac{14575}{100} = 145.75$$

The cost of living has increased by 45.75% (145.75 − 100) in the current period compared with the base period.

Example 11: COLI from Group Indices

Group	Food	Clothing	Light	Rent	Fuel	Misc.	Total
Group index $(I)$	410	450	300	370	200	280
Weight $(W)$	40	15	7	10	10	18	100
$WI$	16400	6750	2100	3700	2000	5040	35990

$$\begin{aligned} \text{COLI} &= \frac{\sum WI}{\sum W} = \frac{35990}{100} = 359.90 \\ \text{Salary in 2003} &= 5{,}000 + 259.90\% \text{ of } 5{,}000 = 5{,}000 + 12{,}995 = \text{Rs. } 17{,}995 \end{aligned}$$

The cost of living has increased by 259.90% (359.90 − 100) in 2003 compared with 1995, so a salary of Rs. 5,000 in 1995 should rise in the same ratio to Rs. 17,995.

Example 12: Real Wages

Year	Monthly wage (Rs.)	Price index	Real wage $= \frac{\text{Wage}}{\text{Price index}} \times 100$
1995	3600	100	3600
1996	4000	104	3846.15
1997	4800	115	4173.91
1998	5200	160	3250
1999	5500	210	2619.05
2000	5900	260	2269.23

The real wage was highest in 1997 and lowest in 2000, even though the money wage rose every year.

Example 13: Real Wage Index

Year	Wage (Rs.)	Price index	Real wage	Real wage index
2000 (base)	180	100	180	100
2001	230	170	135.29	75.16
2002	340	300	113.33	62.96
2003	360	320	112.50	62.50
2004	365	330	110.61	61.45
2005	370	340	108.82	60.46
2006	375	350	107.14	59.52

Real wage index = (real wage of the year ÷ 180) × 100.

Example 14: Does the Worker Gain?

A worker earned Rs. 300 when the price index was 100. The index has risen to 200 and the wage to Rs. 500.

The index has increased by 100% (200 − 100), so the wage should increase in the same ratio: required wage = 300 + 100% of 300 = Rs. 600. Since the wage paid (Rs. 500) is less than the required Rs. 600, the worker does not gain.

Important Questions

2078 Exam

Find the simple aggregative price index number for the year 2021: [2 marks]

Commodities A B C D E

Price in 2020 10 20 18 15 12

Price in 2021 15 22 20 22 18
The following table gives the changes in the price and the consumption (quantity) of certain major constituents of the consumption basket of the labour class. [10 marks]

Commodity Unit 2020 Price 2020 Qty 2021 Price 2021 Qty

Wheat Quintals 1000 10 1100 6

Rice Quintals 1500 15 1700 18

Cloth Metres 50 50 40 30

Commodities	A	B	C	D	E
Price in 2020	10	20	18	15	12
Price in 2021	15	22	20	22	18

Commodity	Unit	2020 Price	2020 Qty	2021 Price	2021 Qty
Wheat	Quintals	1000	10	1100	6
Rice	Quintals	1500	15	1700	18
Cloth	Metres	50	50	40	30

2079 Exam

Find the simple aggregative price index number for the year 2021 from the following information. [2 marks]

Commodities A B C D E F

Price in 2020 (Rs.) 160 140 150 130 155 120

Price in 2021 (Rs.) 170 135 155 140 150 30

Commodities	A	B	C	D	E	F
Price in 2020 (Rs.)	160	140	150	130	155	120
Price in 2021 (Rs.)	170	135	155	140	150	30

2080 Exam

Find the simple aggregative price index number from the following data of 2015, taking 2014 as the base year, when current year quantity is taken as weight. [2 marks]

Commodities Price in 2014 Price in 2015

A 5 8

B 4 6

C 10 12

D 7 5
An inquiry into the budget of middle class families in a certain city gave the following information: [10 marks]

Expenses Food Fuel Clothing Rent Miscellaneous

Weight 35% 10% 20% 15% 20%

Price in 2015 145 23 65 30 40

Price in 2016 150 25 75 30 45

What is the cost of living index number of 2016 as compared with that of 2015? If an employee's salary of Rs. 20,000 per month is raised to Rs. 21,000 in 2016, is it adequate? If not, what should be the increment in salary in 2016?

Commodities	Price in 2014	Price in 2015
A	5	8
B	4	6
C	10	12
D	7	5

Expenses	Food	Fuel	Clothing	Rent	Miscellaneous
Weight	35%	10%	20%	15%	20%
Price in 2015	145	23	65	30	40
Price in 2016	150	25	75	30	45

2081 Exam

Find the simple aggregative price index number from the following data: [2 marks]

Commodities A B C D

Price in 2022 45 58 35 20

Price in 2023 55 50 32 28
The following table gives the changes in the price (in Rs.) and the quantity (units) of certain commodities: [10 marks]

Commodity 2022 Price 2022 Quantity 2023 Price 2023 Quantity

A 1200 15 1500 17

B 1700 20 1800 16

C 500 50 400 60

D 100 25 120 30

Calculate the price index number according to (a) Laspeyres' formula, (b) Paasche's formula, (c) Fisher's ideal formula.
(a) Solve the following linear programming problem graphically: [10 marks]

$$\begin{aligned} \text{Maximize } Z &= 4x + 3y \\ \text{subject to } 2x + y &\le 10 \\ x + y &\le 6 \\ x,\ y &\ge 0 \end{aligned}$$

(b) The following table is the conditional payoff table:

Strategy State A State B State C State D

$S_1$ 200 210 240 220

$S_2$ 180 220 220 210

$S_3$ 270 200 340 280

$S_4$ 260 180 300 120

$S_5$ 250 190 240 200

Provide a decision according to (i) maximax criterion, (ii) maximin criterion, (iii) minimax regret criterion.

Commodities	A	B	C	D
Price in 2022	45	58	35	20
Price in 2023	55	50	32	28

Commodity	2022 Price	2022 Quantity	2023 Price	2023 Quantity
A	1200	15	1500	17
B	1700	20	1800	16
C	500	50	400	60
D	100	25	120	30

Strategy	State A	State B	State C	State D
\(S_1\)	200	210	240	220
\(S_2\)	180	220	220	210
\(S_3\)	270	200	340	280
\(S_4\)	260	180	300	120
\(S_5\)	250	190	240	200

2082 Exam

Find the simple aggregative price index number for the year 2023 from the following information: [2 marks]

Commodities A B C D E

Price in 2022 15 25 23 25 17

Price in 2023 18 27 25 28 20
The following table gives the changes in price and quantity of the consumption basket of the labour class. [10 marks]

Commodity 2022 2023

Price Quantity Price Quantity

A 1200 10 1500 11

B 1700 12 1800 18

C 500 50 700 60

D 300 40 500 50

Calculate the cost of living index. If the average labour wage was Rs. 24,000 per month in 2022, what should be the average wage per worker per month in 2023 so that the standard of living of the workers does not fall below the 2022 level?

Commodities	A	B	C	D	E
Price in 2022	15	25	23	25	17
Price in 2023	18	27	25	28	20

Commodity	2022	2023
A	1200	10	1500	11
B	1700	12	1800	18
C	500	50	700	60
D	300	40	500	50

2083 Exam

Calculate the price index number of a group of four commodities by using (a) Laspeyres' formula, (b) Fisher's formula and (c) Paasche's formula: [15 marks]

Commodity Base year Current year

Price/unit Expenditure Price/unit Expenditure

A 2 40 5 75

B 4 16 8 40

C 1 10 2 24

D 5 25 10 60

Also examine whether the time reversal test and the factor reversal test are satisfied by Fisher's index number.

Feature	Laspeyres'	Paasche's	Fisher's
Weight used	Base year quantity \(q_0\) only	Current year quantity \(q_1\) only	Both base year and current year quantities
Time reversal test	Not satisfied	Not satisfied	Satisfied
Factor reversal test	Not satisfied	Not satisfied	Satisfied

Commodity	A	B	C	D	E	Total
Price in 2020 \((p_0)\)	10	20	18	15	12	75
Price in 2021 \((p_1)\)	15	22	20	22	18	97

Index	\(P_{01} \times P_{10}\)	Time reversal test	\(P_{01} \times Q_{01}\)	Factor reversal test
Laspeyres'	\(\frac{202}{91} \times \frac{92}{199} = 1.026\)	Not satisfied	\(\frac{202}{91} \times \frac{92}{91} = 2.244\)	Not satisfied
Paasche's	\(\frac{199}{92} \times \frac{91}{202} = 0.974\)	Not satisfied	\(\frac{199}{92} \times \frac{199}{202} = 2.131\)	Not satisfied
Fisher's	1	Satisfied	\(\frac{199}{91} = 2.187\)	Satisfied

Item	A	B	C	D	E	Total
% of expenditure \((W)\)	25	35	15	10	15	100
Price relative \((P)\)	125	140	160	130	190
\(PW\)	3125	4900	2400	1300	2850	14575

Group	Food	Clothing	Light	Rent	Fuel	Misc.	Total
Group index \((I)\)	410	450	300	370	200	280
Weight \((W)\)	40	15	7	10	10	18	100
\(WI\)	16400	6750	2100	3700	2000	5040	35990

Commodity	2022		2023
Commodity	Price	Quantity	Price	Quantity
A	1200	10	1500	11
B	1700	12	1800	18
C	500	50	700	60
D	300	40	500	50

Commodity	Base year		Current year
Commodity	Price/unit	Expenditure	Price/unit	Expenditure
A	2	40	5	75
B	4	16	8	40
C	1	10	2	24
D	5	25	10	60

Business Statistics

Business Statistics