Exercises
Question 1
The average retail price prices in pounds per tonne of coal sold in Great Britain during the years 1992-1997 are given in Table 1.
a) using 1992 as a base, find the price relatives corresponding to the years 1995 and 1997. 
b) using 1995 as a base, find the price relatives corresponding to all the given years.
c) using 1994 as a base, find the price relatives corresponding to all the given years. 
Table 1
Year	Average retail price of coal  (pounds per tonne)	
1992	14.95	
1993	14.94	
1994	15.10	
1995	15.65	
1996	16.28	
1997	16.53	
Question 2
In Table 2 are given data on the production of wheat in  France, in millions of Kg for the years 1989-1997. Reduce the data to quantity relatives using a) 1994 and b) 1989 as a base.
Table 2 
Year	Production of Wheat (Millions of kg)	
1989	1019	
1990	988	
1991	1306	
1992	1173	
1993	984	
1994	935	
1995	1004	
1996	951	
1997	1462	
Question 3.
Customers of the Statisticians Arms have a rather limited choice of beverages, being restricted to beer, whisky or tomato juice. The prices of these items, and the consumption by customers, for 1996 and 1997 are as follows:
Table 3
	1996	1997	
	Price	Quantity	Price	Quantity	
Beer (pint)	130	60,000	140	55,000	
Whisky (single)	165	20,000	180	21,000	
Tomato (small)	55	15,000	75	18,000	
Calculate a base-weighted and a current-weighted price index for this data in 1997, using 1996 a base-year.

Question 4.
Find the (a) Current-year (Laspeyres) and (b) Base-weighted (Paasche) index numbers for the data of  Table 4. c) State an advantage of the Laspeyres index over the paasche index in case revisions of an index number are to be made from year to year.
Table 4
	Prices			Quantities	
	1988	1997		1988	1997	
Coal	£20.13	£28.20		3.559	1.821	
	per tonne	per tonne		million tonnes	million tonnes	
Petrol	£20.3	£21.4		80.2	118.6	
	per litre	per litre		million barrels*	million barrels*	
* Each barrel contains 159 litres.
Question 5.
A company employs three grades of male direct operators, M1, M2 and M3 and three grades of direct female operators, F1, F2, and f3. The following table gives the number of operators employed and the rates paid.
Table 5
		1996 		1997	
Labour		Rate	No of		Rate	No of	
Grade 		per hour	Ops		per hour	Ops	
M1		0.66	32		0.80	35	
M2		0.62	14		0.74	10	
M3		0.56	16		0.66	12	
F1		0.44	40		0.64	45	
F2		0.41	18		0.58	16	
F3		0.36	25		0.52	30	
With 1996 as base calculate an index number for the average wage in 1997 using
a) base weighting, and
b) current weighting
Comment on the relationship between the two indices.