Fit a trend line by the method of freehand method for the given data

Year	2000	2001	2002	2003	2004	2005	2006	2007
Sales	30	46	25	59	40	60	38	65

What is the need for studying time series?

Define secular trend.

Find the trend of production by the method of a five-yearly period of moving average for the following data:

Year	1979	1980	1981	1982	1983	1984	1985	1986	1987	1988	1989	1990
Production(‘000)	126	123	117	128	125	124	130	114	122	129	118	123

Write note on Fisher’s price index number.

State the uses of Cost of Living Index Number.

Using Fisher’s Ideal Formula, compute price index number for 1999 with 1996 as base year, given the following:

Year	Commodity: A		Commodity: B		Commodity: C
	Price (Rs.)	Quantity (Kg)	Price (Rs.)	Quantity (Kg)	Price (Rs.)	Quantity (Kg)
1996	5	10	8	6	6	3
1999	4	12	7	7	5	4

Define a control chart.

Write the control limits for the R chart.

Using the method ofleast squares, fit a straight line trend for Σx = 10, Σy = 16.9, Σx² = 30, Σxy = 47.4 and n = 7.

Calculate the 3-yearlymoving averages of the production figures (in tonnes) for the following data.

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

Calculate the seasonal indices by the method of simple average for the following data.

Year	I quarter	II quarter	III quarter	IV quarter
1985	68	62	61	63
1986	65	58	66	61
1987	68	63	63	67

Calculate the cost of living index by aggregate expenditure method

Commodity	Quantity	Price(Rs.)
	2000	2000	2003
A	100	8	12
B	25	6	7.50
C	10	5	5.25
D	20	48	52
E	65	15	16.50
F	30	19	27.00

Construct the cost of living index for 2003 on the basis of 2000 from the following data using family budget method.

Item	Price(Rs.)		Weights
Food	2000	2003	30
Rent	200	280	30
Clothing	150	120	20
Fuel & lighting	50	100	10
Miscellaneous	100	200	20

The following data shows the value of sample mean (\(\bar{X}\)) and the range R for 10 samples of size 5 each. Calculate the control limits for : mean chart and range chart.

Sample No.	1	2	3	4	5	6	7	8	9	10
Mean \(\bar{X}\)	11.2	11.8	10.8	11.6	11.0	9.6	10.4	9.6	10.6	10.0
Range	7	4	8	5	7	4	8	4	7	9

(Given for n = 5, A₂ = .577, D₃ = 0, D₄ = 2.115)