The use or application of a particular average depends upon the purpose of the investigation. Some of the cases of different averages are as follows:
Arithmetic mean is considered an deal average. It is frequently used in all the aspects of life. It possesses many mathematical properties and due to this it is of immense utility in further statistical analysis. In economic analysis arithmetic mean is used extensively to calculate average production, average wage, average cost, per capital income exports, imports, consumption, prices, etc. When different items of a series have different relative importance, then weighted arithmetic mean is used.
Use of Geometric mean is important in a series having items of wide dispersion. It is used in the construction of index number. The averages of proportions, percentages and compound rates are computed by geometric mean. The growth of population is measured in it as population increases in geometric progression.
Harmonic mean is applied in the problems where small items must get more relative importance than the large ones. It is useful in cases where time, speed, values given in quantities, rate and prices are involved. But in practice, it has little applicability.
Median and partition Values
Median and partition values are positional measures of central tendency. There are mainly used in the qualitative cases like honestly, intelligence, ability, etc. In the distributions which are positively skewed, median is a more suitable average. These are also suitable for the problems of distribution of income, wealth, investment, etc.
Mode is also positional average. Its applicability of daily problems is increasing. Mode is used to calculate the 'modal size of a collar', 'modal size of shore', or 'modal size of ready-made garments' etc. It is also used in the sciences of Biology, Meteorology, Business and Industry.