Page 244 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes 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.
18.2 Merits and Limitations of Simple Average of Price Relative Method

Merits

This method has the following two advantages over the previous method:
1. Extreme items do not influence the index. Equal importance is given to all the items.
2. 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.
Limitations

Despite these merits this method is not very satisfactory because of two reasons:
1. 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.
2. 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.
Self-Assessment

1. Fill in the Blanks:
(i) Theoretically the best average in the construction of index number is.
(ii) A price relative is the percentage ratio of the price of a variable in the ......... year to the price
in the ......... year.
(iii) Weighted average of relatives can be combined to form a new ......... .
(iv) The index is not influenced by the unit in which ......... are quoted.
(v) The average may be arithmetic mean, median, mode or ......... .
18.3 Summary

• The arithmetic average has the advantage of simplicity but it is too much affected by the extreme
values. It gives too much weight to increasing prices and little to decreasing ones. According to
this method, we first find out price relative for each commodity and then take simple average
of all price relatives. A price relative is the percentage ratio of the price of a variable in the
current year to the price in the base year.
• The Geometric Mean is used when items in a group are considered from the view point of their relative
difference rather than that of their absolute difference. For example, if the price of a commodity

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