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

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

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

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

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)

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

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
	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

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

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

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

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

Commodity	Price		Quality
	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

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

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

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)

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)

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
	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