QB365 provides a detailed and simple solution for every Possible Creative Questions in Class 12 Business Maths Subject - Applied Statistics, English Medium. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

Download Tamil Nadu 12th Standard Business Maths and Statistics question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

Questions:

Generic 5

15 x 5 = 75

Construct Fisher's price index number and prove that it satisfies both Time Reversal Test and Factor Reversal Test for data following data.

Commodities	Base year		Current year
Commodities	Price	Quantity	Price	Quantity
Rice	11	6	2	8
Wheat	6	5	5	10
Rent	5	10	4	14
Fuel	2	13	2	19
Transport	50	5	65	8
Miscellaneous	75	1	80	3

The following are the X and R values for 20 samples of 5 readings. Draw x chart and R chart and write your conclusion

Sample	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
\(\bar X\)	34	31.6	30.8	33	35	33.2	33	32.6	33.8	37.8	35.8	38.4	34	35	38.8	31.6	33	28.2	31.8	35.6
R	4	4	2	3	5	2	5	13	19	6	4	4	14	4	7	5	5	3	9	6

(Given for n = 5, A₂ = 0.58, D₃ = 0, D₄= 2.12)

The following data relate to the life in hours of 10 samples of 6 electric bulbs each drawn at an interval of one hour from a production process. Draw chart for \(\bar X\) and R and comment.

Sample no	Life Time (in hours)
1	620	687	666	689	738	686
2	501	584	524	585	653	668
3	673	701	686	567	619	660
4	646	626	572	628	631	743
5	494	984	659	643	660	640
6	634	755	625	582	683	555
7	519	710	664	693	770	531
8	630	723	614	535	550	570
9	482	791	533	612	497	499
10	706	524	626	503	661	754

(Given for n = 6, A₂= 0.483, D₃ = 0, D₄= 2.004)

Calculate the cost of living index number using family budget method

Commodity	A	B	C	D	E	F	g	H
Quantity in base year (unit)	20	50	50	20	40	50	60	40
Price in base year (Rs)	10	30	40	200	25	100	20	150
Price in current year (Rs)	12	35	50	300	50	150	25	180

Construct the price index number form the following data by applying
i) Laspeyre's
(ii) Paasche's and
(ii) Fisher's method

Commodity	1999		1998
Commodity	Price	Quantity	Price	Quantity
A	11	6	2	8
B	6	5	5	10
C	5	10	4	14
D	2	13	2	19

Compute
(i) Laspeyre's
(ii) Paasche's and
(iii) Fisher's index number

Commodity	Price		Quality
Commodity	Base year	current year	Base year	current year
A	6	10	50	50
B	2	2	100	120
C	4	6	60	60
D	10	12	30	25

Compute index number using Fisher's formula and show that it satisfies time reversal and factor reversal test.

Commodity	Base year		Current year
Commodity	1985	1986	1985	1986
A	10	12	12	15
B	7	15	5	20
C	5	24	9	20
D	16	15	14	5

Calculate Fisher's ideal index from the following data and verify that it satisfies both time Reversal and Faetor Reversal test.

Commodity	Price		Quantity
Commodity	1985	1986	1985	1986
A	8	20	50	60
B	2	6	15	10
C	1	2	20	25
D	2	5	10	8
E	1	5	40	30

From the following data, calculate price index number by
(a) Laspeyre's method
(b) Paasche's method
(c) Fisher's method

Commodity	Base year		Current year
Commodity	Price	Quantity	Price	Quantity
A	2	40	6	50
B	4	50	8	40
C	6	20	9	30
D	8	10	6	20
E	10	10	5	20

10.

Calculate the 3 yearly moving average of the production figures given below

Year	1973	1974	1975	1976	1977	1978	1979	1980	1981	1982	1983	1984	1985	1986	1987
Production	15	21	30	36	42	46	50	56	63	70	74	82	90	95	102

11.

The followingdata relateto the life(inhours) of 10 samples of 6 electricbulbs each drawn at an intervalof one hour from a production process.Draw the controlchart for \(\overline { X } \) and \(\overline { R } \) and comment.

Sample No	Lifetime (inhour)
	1	2	3	4	5	6
1	620	687	666	689	738	686
2	501	585	524	585	653	668
3	673	701	686	567	619	660
4	646	626	572	628	631	743
5	494	984	659	643	660	640
6	634	755	625	582	683	555
7	619	710	664	693	770	534
8	630	723	614	535	550	570
9	482	791	533	612	497	499
10	706	524	626	503	661	754

(For n = 6,A₂= 0.483,D₃ = 0,D₄ = 2.004)

12.

Calculate Fisher's ideal index from the following data and verify that it satisfies both time reversal and factor reversal test

Commodity	Price		Quantity
	1985	1986	1985	1986
A	8	20	50	60
B	2	6	15	10
C	1	2	20	25
D	2	5	10	8
E	1	5	40	30

13.

Compute
(i) Laspeyre's
(ii) Paasche's
(iii) Fisher's price index number for 2000 from the following data.

Commodity	Price		Quantity
	1990	2000	1990	2000
A	2	4	8	6
B	5	6	10	5
C	4	5	14	10
D	2	2	19	13

14.

From the data given below, calculate seasonal indices.

Quarter	Year
	1984	1985	1986	1987	1988
I	40	42	41	45	44
II	35	37	35	36	38
III	38	39	38	36	38
IV	40	38	40	41	42

15.

Fit a straight line trend to the following data using the method of least square. Estimate the trend for 2007.

year	2000	2001	2002	2003	2004
Sales (in tonnes)	1	1.8	3.3	4.5	6.3

Visit QB365-SLMS - https://www.qb365.in/slms/

Answers Key:

Generic 5

15 x 5 = 75

Commodities	1999		1998		p_oq_o	\(p_{0} q_{1} \)	\( p_{1} q_{0} \)	\(p_{1} q_{t}\)
Commodities	Price (p_o)	Quantity (q_o)	Price (p₁)	Quantity (q₁)	p_oq_o	\(p_{0} q_{1} \)	\( p_{1} q_{0} \)	\(p_{1} q_{t}\)
Rice	25	5	45	4	125	100	225	180
Wheat	45	2	42	3	90	135	84	126
Rent	90	4	95	6	360	540	380	570
Fuel	65	3	50	2	195	130	150	100
Transport	50	5	65	8	250	400	325	520
Miscellaneous	75	1	80	3	75	225	80	240
Total					1095	1530	1244	1736

Fishers price index number
\( =\left(\sqrt{\frac{\sum P_{1} q_{0} \times \sum P_{1} q_{1}}{\sum P_{0} q_{0} \sum P_{0} q_{1}}}\right) \times 100 \)
\( =\sqrt{\frac{1344}{1005} \times \frac{1735}{1530}} \mathbf{x} 100=1.2890 \times 100\)
\(\mathrm{P}_{01}^{\bar{F}}=128.90\)
Time Reversal Test :
\( \mathrm{P}_{01} \times \mathrm{P}_{10}=1 \)
\(P_{01} \times P_{10}=\sqrt{\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{a}} \times \frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}} \times \frac{\sum q_{1} p_{0}}{\sum q_{0} p_{0}} \times \frac{\sum q_{1} p_{1}}{\sum q_{0} p_{1}}}\\ \)
\( =\sqrt{\frac{1244}{1095} \times \frac{1736}{1530} \times \frac{1530}{1095} \times \frac{1736}{1344}} \)
\( =\sqrt{\frac{1736 \times 1736}{1095 \times 1095}}=\frac{1736}{1095} \)
\( P_{01} \times Q_{01}=\frac{\sum P_{1} q_{1}}{\sum P_{0} q_{0}} \)

\( \overline{\bar{X}}=\frac{\sum \bar{X}}{n}=\frac{6 \pi 7}{20}=33.85 \)
\(\bar{R}=\frac{\sum R}{n}=\frac{124}{20}=6.2 \)
Control limit for \(\bar X\) chart
\(\mathrm{UCL}=\overline{\bar{X}}+A_{2} \bar{R}\)
= 33.85 + 0.58 (6.2) = 37.446
\(\mathrm{LCL}=\overline{\bar{X}}-A_{2} \bar{R}^{1}\)
\(=33.85-(0.58)(6.2)=30.254\)
CL = 33.85
Control limit for R chart
\( \bar{R} =\mathrm{CL}=6.2 \)
\(\mathrm{UCL} =D_{i} \bar{R} \)
\( =(2.12)(6.2)=13.141 \)
\(\mathrm{LCL} =D_{3} \bar{R}=0\)

Since points lie outside the UCL are of x and R chart, the process is not in control.

Sample No	Total	Sample Mean \(\bar X\)	Sample Range R
1	4086	681	118
2	3516	586	117
3	3906	651	134
4	3846	641	171
5	4080	680	490
6	3834	639	200
7	3990	665	200
8	3622	604	188
9	3414	569	309
10	3774	629	257

\( \overline{\bar{X}} =\frac{\sum \bar{X}}{n} \)
\(=\frac{6345}{10}=634.5 \)
\(\bar{R} =\frac{\sum R}{n} \)
\( =\frac{2264}{10}=226.4 \)
Control limits for \(\bar X\) chart
\( \mathrm{UCL} =\overline{\bar{X}}+A_{2} \bar{R} \)
\( =634.5+(0.483)(226.4) \)
\( =634.5+109.35 \)
\( =743.85 \)
\(\mathrm{CL} =634.5 \)
\(\mathrm{LCC} =\overline{\bar{X}}-A_{2} \bar{R} \)
\( =634.5-109.35 \)
\( =525.15 \)
Control limits for R chart
\( \mathrm{UCL}^{\cdot} =D_{4} \bar{R} \)
\( =2.004 \times 226.4 \)
\( =453.7056 \)
\( \mathrm{LCL} =D_{3} \bar{R}=0 \)
\(\mathrm{CL} =226.4 .\)

Since one of the points of the sample range. in outside the UCL of R chart, the process is not in control.

Commodity	Price		Quantity (V)	\(\mathrm{P}=\frac{P_{1}}{P_{0}} \times 100\)	PV
Commodity	Base year p_o	Current year p₁	Quantity (V)	\(\mathrm{P}=\frac{P_{1}}{P_{0}} \times 100\)	PV
A	10	12	20	120	2400
B	30	35	50	116.67	5833.50
C	40	50	50	125	6250
D	200	300	20	150	3000
E	25	50	40	200	8000
F	100	150	50	150	7500
G	20	25	60	125	7500
H	150	180	40	120	4800
			330		45283.50

Cost of Living index
\(=\frac{\sum P V}{\sum V}=\frac{45283.50}{330}=137.22\)

Commodity	1999		1998		p_oq_o	\(p_{0} q_{1} \)	\( p_{1} q_{0} \)	\(p_{1} q_{t}\)
Commodity	Price	Quantity	Price	Quantity	p_oq_o	\(p_{0} q_{1} \)	\( p_{1} q_{0} \)	\(p_{1} q_{t}\)
A	11	6	2	8	16	32	12	24
B	6	5	5	10	50	60	25	30
C	5	10	4	14	56	70	40	50
D	2	13	2	19	38	38	26	26
					160	200	103	130

Laspeyre's index Number \( =\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times 100 \)
\(=\frac{200}{160} \times 100=125 \)
Paasche's index Number = \(p_{01}^{P}\)
\( =\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}} \times 100 \)
\( =\frac{130}{103} \times 100=126.21 \)
Fisher's index Number
\(=\sqrt{p_{01}^{L} \times p_{01}^{p}}=\sqrt{125 \times 126.21}=125.6\)

Commodity	Price		Quality		p_oq_o	\(p_{0} q_{1} \)	\( p_{1} q_{0} \)	\(p_{1} q_{t}\)
Commodity	p_o	q_o	p₁	q₁	p_oq_o	\(p_{0} q_{1} \)	\( p_{1} q_{0} \)	\(p_{1} q_{t}\)
A	6	10	50	50	300	500	300	500
B	2	2	100	120	200	200	240	240
C	4	6	60	60	240	360	240	360
D	10	12	30	25	300	360	250	300
Total					1040	1420	1030	1400

Laspeyre's Index Number
\(=\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times 100=\frac{1420}{1040} \times 100=136: 54\)
Paasche's Index Number = \(P_{01}^{P}\)
\(=\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}} \times 100=\frac{1420}{1030} \times 100=135.92\)
Fisher's Index Number
\(=\sqrt{P_{01}^{L} \times P_{01}^{p}}=\sqrt{136.54 \times 135.92}=136.23\)

Commodity	Base year		Current year		\( p_{0} q_{0} \)	\(p_{0} q_{1} \)	\( p_{1} q_{0} \)	\(p_{1} q_{1}\)
Commodity	1985	1986	1985	1986	\( p_{0} q_{0} \)	\(p_{0} q_{1} \)	\( p_{1} q_{0} \)	\(p_{1} q_{1}\)
A	10	12	12	15	144	120	180	150
B	7	15	5	20	75	105	100	140
C	5	24	9	20	216	120	180	100
D	16	15	14	5	70	80	70	80
Total					505	425	530	570

Fisher's index Number :
\( =\sqrt{\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times \frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}}} \times 100 \)
\( =\sqrt{\frac{505}{425}, \frac{530}{4 / 0} \times 100}=115.75 \)
Time Reversal Test :
Test is satisfied when \(P_{01} \times P_{10}=1\)
\( P_{01} \times P_{10}=\sqrt{\frac{\Sigma p_{1} q_{0}}{\Sigma p_{1} q_{0}} \times \frac{\Sigma p_{q_{1}}}{\Sigma p_{0} q_{1}} \times \frac{\Sigma p_{1} q_{1}}{\Sigma p_{q_{1}}} \times \frac{\Sigma p_{1} q_{0}}{\Sigma p_{q_{1}}}} \)
\( =\sqrt{\frac{505}{425} \times \frac{530}{470} \times \frac{470}{530} \times \frac{425}{505}}=1 \)
Hence Fisher's index Number satisfies Time Reversal Test
Factor Reversal Test :
Test is satisfied when
\( P_{01} \times Q_{01} =\frac{\Sigma p_{1} q_{1}}{\Sigma_{p_{0} q_{0}}} \)
\(P_{01} \times Q_{01} =\sqrt{\frac{\Sigma p_{1} q_{0}}{\Sigma p_{0} q_{0}} \times \frac{\Sigma p_{1} q_{1}}{\Sigma p_{1} q_{1}} \times \frac{\Sigma p_{0} q_{1}}{\Sigma p_{0} q_{0}} \times \frac{\Sigma p_{1} q_{1}}{\Sigma q_{1} q_{0}}} \)
\( =\sqrt{\frac{505}{425} \times \frac{530}{470} \times \frac{470}{425} \times \frac{530}{505}} \)
\( =\frac{530}{425}=\frac{\Sigma p_{0} q_{1}}{\Sigma p_{0} q_{0}}\)
Hence Fisher's index Number satisfies factor Reversal Test.

Commodity	Price		Quantity		\( p_{0} q_{0} \)	\(p_{0} q_{1} \)	\( p_{1} q_{0} \)	\(p_{1} q_{1}\)
Commodity	1985	1986	1985	1986	\( p_{0} q_{0} \)	\(p_{0} q_{1} \)	\( p_{1} q_{0} \)	\(p_{1} q_{1}\)
A	8	20	50	60	400	480	1000	1200
B	2	6	15	10	30	20	90	60
C	1	2	20	25	20	25	40	50
D	2	5	10	8	20	16	50	40
E	1	5	40	30	40	30	200	150
Total					510	570	1380	1500

Fisher's index number
\( =\sqrt{\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times \frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}}} \times 100 \)
\( =\sqrt{\frac{1380}{510} \times \frac{1500}{571}} \times 100 \\ \)
\(=2.6661 \times 100=266.61\)
Time Reversal Test :
Test is satisfied when \(p_{01} \times p_{10}=1\)
\( P_{01} \times P_{10} =\sqrt{\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times \frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}} \times \frac{\sum p_{0} q_{1}}{\sum p_{1} q_{1}} \times \frac{\sum p_{0} q_{0}}{\sum p_{1} q_{1}}} \)
\( =\sqrt{\frac{1380}{510} \times \frac{1500}{571} \times \frac{571}{1500} \times \frac{510}{1380}}=1 \)
Fisher's index number satisties Time Reversal Test
Factor Reversal Test :
Test is satisfies when
\( P_{01} \times P_{01} =\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{0}} \)
\(P_{01} \times P_{01} =\sqrt{\frac{\Sigma p_{1} q_{0}}{\Sigma p_{0} q_{0}} \times \frac{\Sigma p_{1} q_{1}}{\sum p_{0} q_{1}} \times \frac{\sum p_{0} q_{1}}{\Sigma p_{0} q_{0}} \times \frac{\Sigma_{p_{1} q_{1}}}{\Sigma_{1} q_{0}}} . \\ \)
\(=\sqrt{\frac{1380}{510} \times \frac{1500}{571} \times \frac{571}{510} \times \frac{1500}{1380}} \)
\( =\frac{1500}{510}=\frac{\sum p_{0} q_{1}}{\sum p_{0} q_{0}}\)
Hence Fishers index satisfies Factor Reversal Test

Commodity	Base year		Current year		\( \mathrm{p}_{0} \mathrm{q}_{0} \)	\( \mathrm{p}_{1} \mathrm{q}_{0} \)	\( p_{0} \mathrm{q}_{1} \)	\( \mathrm{p}_{1} \mathrm{q}_{1}\)
Commodity	Price p_o	Quantity q_o	Price p₁	Quantity q₁	\( \mathrm{p}_{0} \mathrm{q}_{0} \)	\( \mathrm{p}_{1} \mathrm{q}_{0} \)	\( p_{0} \mathrm{q}_{1} \)	\( \mathrm{p}_{1} \mathrm{q}_{1}\)
A	2	40	6	50	80	240	100	300
B	4	50	8	40	200	400	160	320
C	6	20	9	30	120	180	180	270
D	8	10	6	20	80	60	160	120
E	10	10	5	20	100	50	200	100
					580	930	800	1110

Laspeyre's index number \(=p_{01}^{L}\)
\( =\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times 100 \)
\(=\frac{930}{580} \times 100=160.34 \)
Paasche's index number \(=p_{01}^{L}\)
\( =\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}} \times 100 \)
\( =\frac{1100}{800} \times 100=138.75\)
Fisher's index number \(=p_{01}^{L}\)
\(=\sqrt{p_{01}^{L} \times p_{01}^{P}}=149.15\)

10.

Year	Production	3 yearly moving total	3 yearly moving average
1973	15	-	-
1974	21	66	22
1975	30	87	29
1976	36	108	36
1977	42	124	41.33
1978	46	138	46
1979	50	152	50.67
1980	56	169	56.33
1981	63	189	63
1982	70	207	69
1983	74	226	75.33
1984	82	246	75.33
1985	90	267	82
1986	95	287	89
1987	102	-	95.67

11.

Sample No	Total	\(\overline { X } \)	R = X_max- X_min
1	4086	681	118
2	3516	586	167
3	3906	651	134
4	3846	641	171
5	4080	680	490
6	3834	639	200
7	3990	665	236
8	3622	604	188
9	3414	569	309
10	3774	629	251
		6345	2264

\(\bar{\bar{X}}\) = 634.5, \(\bar{R}\) = 226.4
Control limits for \(\overline { X } \) - chart are
UCL = \(\bar{\bar{X}}\) + A₂\(\bar{R}\)
= 634.5+ 0.483x 226.4
= 743.85
CL = 634.5
LCL = \(\bar{\bar{X}}\)- A₂\(\bar{R}\) = 525.15
Control limits of R-chart are
UCL = D₄\(\bar{R}\) = 2.004 x226.4
= 453.7056
CL = 226.4
LCL = D_3\(\bar{R}\)= 0
\(\overline { X } \)-chart

R - chart

Conclusion: Since one point in R-chart lie outside the control limits, the given system is not in control

12.

Commodity	1985		1986
	p₀	q₀	p₁	q₁
A	8	50	20	60
B	2	15	6	10
C	1	20	2	25
D	2	10	5	8
E	1	40	5	30

p₁q₀	p₀q₀	p₁q₁	p₀q₁
1000	410	1200	480
90	30	60	20
40	20	50	25
50	20	40	16
200	40	150	30
1380	510	1500	571

Fisher's Ideal Index = \(\sqrt\frac{{\Sigma p_1q_0}\times{\Sigma p_1q_1}}{{\Sigma p_0q_0}\times{\Sigma p_0q_1}}\times100\)
\(= \sqrt\frac{1380\times1500}{510\times571}\times100\)
= 266.61
Time reversaltest:
\(P_{01}\times P_{10}=\sqrt\frac{{\Sigma p_1q_0}\times{\Sigma p_1q_1}\times{\Sigma p_0q_1}\times{\Sigma p_0q_0}}{{\Sigma p_0q_0}\times{\Sigma p_0q_1}\times{\Sigma p_1q_1}\times{\Sigma p_1q_0}}\)

= \(\sqrt{1}=1\)
Hence, time reversal test is satisfied.
Factor reversaltest:
\(P_{01}\times Q_{01}=\sqrt\frac{{\Sigma p_1q_0}\times{\Sigma p_1q_1}\times{\Sigma q_1p_0}\times{\Sigma q_1p_1}}{{\Sigma p_0q_0}\times{\Sigma p_0q_1}\times{\Sigma q_0p_0}\times{\Sigma q_0p_1}}\)

\(P_{01}\times Q_{01}=\frac{{\Sigma p_1q_1}}{{\Sigma p_0q_0}}\)
Hence, Fisher's ideal index satisfies factor reversal test also.

13.

Commodity	Price		Quantity
	Base year p₀	Current year p₁	Base year q₀	Current year q₁
A	2	4	8	6
B	5	6	10	5
C	4	5	14	10
D	2	2	19	13

p₀q₀	p₁q₀	p₀q₁	p₁q₁
16	32	12	24
50	60	25	30
56	70	40	50
38	38	26	26
160	200	103	130

(i) Laspeyre's index number
\(P_{01}^{L} = \frac{\Sigma p_1q_0}{\Sigma p_0q_0}\times100\)
\(=\frac{200}{160}\times100=125\)
(ii) Paasche's Price index number
\(P_{01}^{P} = \frac{\Sigma p_1q_1}{\Sigma p_0q_1}\times100\)
\(=\frac{130}{103}\times100=126.21\)
(iii) Fisher's price index number
\(P_{01}^{F} =\sqrt {{P_{01}^{L}}\times{P_{01}^{P}}}=125.6\)

14.

Year	Quarters
	I	II	III	IV
1984	40	35	38	40
1985	42	37	39	38
1986	41	35	38	40
1987	44	38	38	42
1988	44	38	38	42
Total	212	181	189	201
Average	42.4	36.2	37.8	40.2

Grand average = \(\frac{42.4+36.2+37.8+40.2}{4}\)
= 39.15
Seasonal Index (S.1) = \(\frac{Quarterlyaverage}{Grand average}\times 100\)
Hence,
S.1 or I quarter = \(\frac{42.4}{39.15}\times100=108.30\)
S.1 or II quarter = \(\frac{36.2}{39.15}\times100=92.54\)
S.1 or III quarter = \(\frac{37.8}{39.15}\times100=96.55\)
S.1 or IV quarter = \(\frac{40.2}{39.15}\times100=102.68\)

15.

Year x	Sales y	X = x-2002	XY	X²
2000	1	-2	-2	4
2001	1.8	-1	-1.8	1
2002	3.3	0	0	0
2003	4.5	1	4.5	1
2004	6.3	2	12.6	4
	16.9	0	13.3	10

Let the required equation of the straight line trend is
y = a + bX
Since Σx = 0. \(a = \frac{\Sigma y}{x} = \frac{16.9}{5}\)
\(b = \frac{\Sigma xy}{\Sigma x^2} = \frac{13.3}{10} = 1.33\)
Hence, the straight line trend is
y = 3.38 + 1.33 (x - 2002)
∴ The trend for 2007 is
y_t = 3.38 + 1.33 (2007 - 2002)
⇒  y_t = 3.38 + 1.33 (5)
⇒  y_t = 3.38 + 6.65
⇒  y_t = 10.03