# Indices of the average levels of the phenomena studied - Statistics

## Indices of the average levels of the phenomena studied

The statistical patterns of development of the studied sets of different phenomena are reflected through the mean values ​​or the average values ​​of their indicators. The dynamics of the average indicators of quality characteristics (cost, price, return on assets, productivity, etc.) as a characteristic of their development takes into account not only changes in the specific values ​​of individual units of the aggregate, but also structural, assortment shifts.

Structural shifts are formed under the influence of such factors as the appearance of new types of products (goods) in the markets of producers and consumers, the disappearance of old products, the change in the share of individual goods with different levels of prices and profitability, territorial shifts in the placement of goods with regional price differentiation, seasonal fluctuations, etc. In this regard, the average indicators can not always be used to characterize the dynamics of qualitative characteristics.

When analyzing the change in the average levels of qualitative characteristics, it is possible to use indices of average values ​​to assess the effect of structural shifts on the dynamics of these levels. The average value in this case should be expressed as the average weighted, and the change in this average will be characterized by the ratio of these averages for the reporting and reference periods:

This index is called an index of variable composition, as it reflects not only the change of a certain characteristic X, but also the structure of the aggregate (change in the specific gravity of individual elements of a homogeneous population).

Thus, the average specific consumption of a certain type of raw material (material) per unit of output produced by different enterprises depends not only on the level of its consumption in individual enterprises, but also on the number of products produced by different enterprises. In this regard, the index of specific consumption of raw materials (material) of variable composition reflects the change in the average specific consumption of a particular type of raw material (material) both at the expense of a change in unit consumption at each enterprise, and due to a change in the share of individual enterprises in the total output of products.

On the basis of the variable composition index, the indices of the constant (fixed) composition () of the averaged attribute and the structure index, or structural shifts ():

Both formulas correspond to the generally accepted rule that the structure of the population as a primary attribute when comparing the averaged characteristics is fixed at the level of the reporting period, and the qualitative attribute as secondary when the structure of the population is changed is fixed at the level of the base period. The use of weights of different periods in this case ensures the linking of the indices to the following system:

On the basis of this equality, the influence of each of the factors on the change in the average level of the studied trait is estimated.

If we designate the structure of the aggregate , then the indexes in question take on the following form:

Based on these formulas, you can calculate the absolute change in the average level of the secondary characteristic due to individual factors - the most averaged attribute and structures :

where .

An isolated assessment of the change of one factor with the invariance of the other leads to an underestimation of the so-called effect of a joint change in factors. This effect is usually taken into account in assessing the change in the average level of a characteristic in a fixed-composition index. If we calculate the indices of a fixed composition with the basis weights and the scales, and then compare them, we get an estimate of the effect of the joint change of factors. Numerous calculations show that this effect, as a rule, is very insignificant, therefore it can be neglected.

The effect of structural shifts on the change in the average level of the phenomenon studied is particularly noticeable when compared over long periods of time and under conditions of significant changes in the structure of socio-economic processes. In connection with this, the elimination of the influence of the structural factor in analyzing changes in the mean values ​​of characteristics as indicators of the main trend is a necessary condition for obtaining a realistic estimate and correct conclusions based on index analysis of various complex phenomena.

For example, a comparison of fertility or death rates of a population over a 10-year period without taking into account changes in the sex and age structure of the population will lead to a distorted estimate of the dynamics of this indicator, since its average values ​​are not comparable with each other due to differences in the structures of the populations under study. In such cases, the analyzed indicators should be calculated according to the same, standard sex and age structure of the population. Used in demography for these purposes, the method of standardizing fertility and mortality indicators is in fact a method of constructing an index of constant composition.

Structural changes can lead to paradoxical conclusions based on an index analysis of the average values ​​of macroeconomic indicators. For example, the change in labor productivity as a whole in the industry may be higher than for individual enterprises. In this case, in order to eliminate the influence of the structural factor for estimating the change in the average productivity of labor, one can apply the index in the form of an average of individual indices for enterprises weighted by the number of their employees during the reporting period. The labor productivity index constructed in this way is a modification of the constant composition index.

Statistical guides contain significant information on the most important economic indicators in the territorial context. This information can be used to construct territorial (spatial) indices of average values, for example, yields, wages, price level, etc. These indices are constructed in a manner similar to that discussed above. But this raises the problem of the choice of weights, which must be solved in each particular case, taking into account the chains and depending on the tasks of the study (comparison).

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