Page 219 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes Self Assessment

Multiple Choice Questions:

11. The Laspeyres’s and Paasche’s formulae are generally preferred for the construction of
....................................

(a) Index numbers (b) Frequency table
(c) Pie charts (d) Bar graphs
12. Index numbers are expressed in terms of .

(a) Constant (b) Decimals

(c) Percentages (d) Decimals
13. Laspeyres’s index requires .................................. calculation work than the one with changing
weights in every period.
(a) Simple (b) Complex
(c) Less (d) More

14. In practical situations, neither ............................... nor .......................... change in the same
proportion, the two index numbers are in general different from each other.

(a) Prices, quantities (b) Size, Volume

(c) Price, Value (d) Ratio, Quantity
10.9 Relation between Weighted Aggregative and Weighted
Arithmetic Average of Price Relatives Index Numbers

It will be shown here that, basically, the two types of index numbers, weighted aggregative and
weighted arithmetic average of price relatives, are same and that one type of index number can
be obtained from the other by suitable selection of weights. Since the weighted aggregative
index numbers are easy to calculate and have simple interpretation, they are preferred to weighted
arithmetic average of price relatives indices.
p q
P La 1 0 100
Consider the Laspeyre’s index 01
p q
0 0
p
1 p q
p 0 0
1 p q , p Pw
Rewriting p q as 0 0 we have P La 0 100 (1)
1 0 p 01
0 p q w
0 0
p
P 1 100
Here and w = p0q0
p
0
In a similar way, the other aggregative type of index numbers can also be converted into
average type index numbers.

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