Commodities	Base Year		Current Year		p0q0	p0q1	p1q0	p1q1
	Price (p0)	Quantity (q1)	Price ((p0))	Quantity (q1)
Rice	40	5	48	4	200	160	240	192
Wheat	45	2	42	3	90	135	84	126
Rent	90	4	95	6	360	540	380	570
Fuel	85	3	80	2	255	170	240	160
Transport	50	5	65	8	250	400	325	520
Miscellaneous	65	1	72	3	65	195	72	216
				Total	1220	1600	1341	1784

Fisher’s price index number
\({ P }_{ 01 }^{ F }=\left( \sqrt { \frac { \sum { { p }_{ 1 }{ q }_{ 10 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } } } \right) \times 100=\left( \sqrt { \frac { 1341\times 1784 }{ 1220\times 1600 } } \right) \times 100=110.706\)
Time Reversal Test:P₀₁x P₁₀=1
\({ P }_{ 01 }\times { P }_{ 10 }=\sqrt { \left( \frac { \sum { { p }_{ 1 }{ q }_{ 0 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } \times \sum { { p }_{ 0 }{ q }_{ 0 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } \times \sum { { p }_{ 1 }{ q }_{ 0 } } } \right) } \)
\({ P }_{ 01 }\times { P }_{ 10 }=\sqrt { \left( \frac { 1341\times 1784\times 1600\times 1220 }{ 1220\times 1600\times 1784\times 1341 } \right) } \)
P₀₁x P₁₀ = 1
Factor Reversal Test
\(P_{01} \times Q_{01}=\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{0}}\)
\(P_{01} \times Q_{01}=\sqrt{\left(\frac{\sum p_{1} q_{0} \times \sum p_{1} q_{1} \times \sum q_{1} p_{0} \times \sum q_{1} p_{1}}{\sum p_{0} q_{0} \times \sum p_{0} q_{1} \times \sum q_{0} p_{0} \times \sum q_{0} p_{1}}\right)}\)
\(P_{01} \times Q_{01}=\sqrt{\left(\frac{1341 \times 1784 \times 1600 \times 1784}{1220 \times 1600 \times 1220 \times 1341}\right)}\)
\(P_{01} \times Q_{01}=\sqrt{\left(\frac{1784 \times 1784}{1220 \times 1220}\right)}=\frac{1784}{1220}\)
\(\Rightarrow P_{01} \times Q_{01}=\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{0}}\)

Commodities	Price		Quandity		p0q0	p0q1	p1q0	p1q1
	2003 (p0)	2009 (q1)	2003 (p0)	2009 (q1)
Rice	10	13	4	6	40	60	52	78
Wheat	125	18	7	8	105	120	126	144
Rent	25	29	5	9	125	225	145	261
Fuel	11	14	8	10	88	110	140	140
Miscellaneous	14	17	6	7	84	98	102	119
Total					442	613	537	742

Fisher’s price index number
\({ P }_{ 01 }^{ F }=\left( \sqrt { \frac { \sum { { p }_{ 1 }{ q }_{ 10 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } } } \right) \times 100=\left( \sqrt { \frac { 537\times 742 }{ 442\times 613 } } \right) \times 100=121.2684\)
Time Reversal Test:P₀₁\(\times\) P₁₀ = 1
\({ P }_{ 01 }\times { P }_{ 10 }=\sqrt { \left( \frac { \sum { { p }_{ 1 }{ q }_{ 0 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } \times \sum { { p }_{ 0 }{ q }_{ 0 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } \times \sum { { p }_{ 1 }{ q }_{ 0 } } } \right) } \)
\({ P }_{ 01 }\times { P }_{ 10 }=\sqrt { \left( \frac { 537\times 742\times 613\times 442 }{ 442\times 613\times 742\times 537 } \right) } \)
\({ P }_{ 01 }\times { P }_{ 10 }=1\)
Factor Reversal Test
\({ P }_{ 01 }\times { Q }_{ 01 }=\frac { \sum { { p }_{ 1 }{ q }_{ 1 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } } \)
\({ P }_{ 01 }\times { P }_{ 01 }=\sqrt { \left( \frac { \sum { { p }_{ 1 }{ q }_{ 0 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } \times \sum { { p }_{ 1 }{ q }_{ 0 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } \times \sum { { p }_{ 0 }{ q }_{ 0 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } } \right) } \)
\({ P }_{ 01 }\times { P }_{ 01 }=\sqrt { \left( \frac { 537\times 742\times 613\times 742 }{ 442\times 613\times 442\times 537 } \right) } \)
\({ P }_{ 01 }\times { P }_{ 01 }=\sqrt { \left( \frac { 742\times 742 }{ 442\times 442 } \right) } =\frac { 742 }{ 442 } \Rightarrow { P }_{ 01 }\times { P }_{ 01 }=\frac { \sum { { p }_{ 1 }{ q }_{ 1 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } } \)

Commodities	Price		Quandity		p0q0	p0q1	p1q0	p1q1
	2000 (p0)	2010 q1	2000 (p0)	2010 (q1)
Rice	38	35	6	7	228	266	210	245
Wheat	12	18	7	10	84	120	126	180
Rent	10	15	10	15	100	150	150	225
Fuel	25	30	12	16	300	400	630	480
Miscellaneous	30	33	8	10	240	300	264	330
				Total	952	1236	1110	1460

Laspeyre’s price index number
\({ P }_{ 01 }^{ L }=\frac { \sum { { p }_{ 1 }{ q }_{ 0 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } } \times 100=\frac { 1110 }{ 952 } \times 100=116.60\)
On an average, there is an increase of 16.60 % in the price of the commodities when the year 2000 compared with the year 2010.
Paasche’s price index number
\({ P }_{ 01 }^{ P }=\frac { \sum { { p }_{ 1 }{ q }_{ 1 } } }{ \sum { { p }_{ 0 }{ q }_{ 1 } } } \times 100=\frac { 1460 }{ 1236 } \times 100=118.12\)
On an average, there is an increase of 18.12 % in the price of the commodities when the year 2000 compared with the year 2010.
Fisher’s price index number
\({ P }_{ 01 }^{ F }=\sqrt { \frac { \sum { { p }_{ 1 }{ q }_{ 0 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } } } \times 100=\sqrt { \frac { 1110\times 1460 }{ 952\times 1236 } } \times 100=117.36\)
On an average, there is an increase of 17.36 % in the price of the commodities when the year 2000 compared with the year 2010.

Computation of seasonal Indices by method of simple averages.
Months Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Year 2001 15 41 25 31 29 47 41 19 35 38 40 30 2002 20 21 27 19 17 25 29 31 35 39 30 44 2003 18 16 20 28 24 25 30 34 30 38 37 39 Monthly Total 53  78 72 78 70 97 100 84 100 115 107 113 Monthly Averages 17.67 26 24 26 23.33 32.33 33.33 28 33.33 38.33 35.67 37.67 S.I for Jan = \(\frac{Monthly\ Average\ (for\ Jan)}{Grand\ average}\times100\)
Grand Average = \(\frac{355.582}{12}=29.63\)
S.I for Jan = \(\frac{17.666}{29.361}\times100=59.62; \) 
S.I for Feb = \(\frac{26}{29.361}\times 100=87.72\)
Similarly other seasonal index values can be obtained.
 
\(\begin{array}{|c|c|} \hline \text { Months } & \text { Seasonal Index } \\ \hline \text { Jan } & 59.62 \\ \hline \text { Feb } & 87.72 \\ \hline \text { Mar } & 80.97 \\ \hline \text { Apr } & 87.72 \\ \hline \text { May } & 78.71 \\ \hline \text { June } & 109.08 \\ \hline \text { July } & 112.45 \\ \hline \text { Aug } & 94.47 \\ \hline \text { Sep } & 112.45 \\ \hline \text { Oct } & 129.32 \\ \hline \text { Nov } & 120.34 \\ \hline \text { Dec } & 127.09 \\ \hline \end{array}\)

Computation of trend values by the method of least squares (ODD Years).

Year(x)	Production of Sugarcane(Y)	X=(x–2003)	X2	XY	Trend values(Yt)
2000	40	-3	9	-120	42.04
2001	45	-2	4	-90	43.07
2002	46	-1	1	-46	44.11
2003	42	0	0	0	45.14
2004	47	1	1	47	46.18
2005	50	2	4	100	47.22
2006	46	3	9	138	48.25
N=7	\(\sum Y\)=316	\(\sum X\)=0	\(\sum X\)2=8	\(\sum XY\)=29	\(\sum Yt\)=316

\(a=\frac { \sum { Y } }{ n } =\frac { 316 }{ 7 } =45.143;\quad b=\frac { \sum { XY } }{ { \sum { X } }^{ 2 } } =\frac { 29 }{ 28 } =1.036\)
Therefore, the required equation of the straight line trend is given by
Y = a + bX
Y = 45.143 + 1.036 (x - 2003)
The trend values can be obtained by
When X = 2000 , Yt = 45.143 + 1.036(2000–2003) = 42.035
When X = 2001, Yt = 45.143 + 1.036(2001–2003) = 43.071,
similarly other values can be obtained.