Page 245 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 18: Methods—Simple Average of Price Relatives

increases by 50% and that of another falls by 50%, the arithmetic average of relatives will neither Notes
rise nor fall implying that there has been no change in the price level. But in fact both the prices
have changed. The Geometric Mean of relatives would in this case show that there has been a
change in the price.
• Although arithmetic mean and geometric mean have both been used, the arithmetic mean is
often preferred because it is easier to compute and much better known. Some economists, notably
F.Y. Edgeworth, have preferred to use the median which is not affected by a single extreme
value. Since the argument is important only when an index is based on a very small number of
commodities, it generally does not carry much weight and the median is seldom used in actual
practice.
• The index is not influenced by the units in which prices are quoted or by the absolute level of
individual prices. Relatives are pure numbers and are, therefore, divorced from the original
units. Consequently, index numbers computed by the relatives method would be the same
regardless of the way in which prices are quoted. This simple average of price relatives is said
to meet what is called the units test.
• Difficulty is faced with regard to the selection of an appropriate average. The use of the arithmetic
mean is considered as questionable sometimes because it has an upward bias. The use of
geometric mean involves difficulties of computation. Other averages are almost never used
while constructing index numbers.
• The relatives are assumed to have equal importance. This is again a kind of concealed weighting
system that is highly objectionable since economically same relatives are more important than
others.
18.4 Key-Words

1. Arithmetic mean : In mathematics and statistics, the arithmetic mean, or simply the mean or
average when the context is clear, is the central tendency of a collection of
numbers taken as the sum of the numbers divided by the size of the
collection. The collection is often the sample space of an experiment. The
term "arithmetic mean" is preferred in mathematics and statistics because
it helps distinguish it from other means such as the geometric and harmonic
mean.
2. Geometric mean : In mathematics, the geometric mean is a type of mean or average, which
indicates the central tendency or typical value of a set of numbers by using
the product of their values (as opposed to the arithmetic mean which uses
their sum). The geometric mean is defined as the nth root (where n is the
count of numbers) of the product of the numbers.
18.5 Review Questions

1. Discuss steps of simple average of price relative method of constructing index numbers.
2. What are the merits and limitations of simple average of price relative method.
3. Explain the role of weights in the construction of general price index numbers.
4. What is simple average of price relative method of constructing index numbers ? Explain by
using arithmetic mean.
5. What is simple average of price relative method of constructing index numbers? Explain by using
geometric mean.

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