Use of G.M. and A.M. in the construction of index numbers

Index numbers are statistical tools used to measure changes in a variable over time. They are widely used in economics, finance, and other fields to track trends and make predictions. In the construction of index numbers, two types of averages are commonly used: geometric mean (G.M.) and arithmetic mean (A.M.).

Advantages of G.M.

The geometric mean is considered the best average in the construction of index numbers for several reasons:

- It reduces the effect of extreme values. Unlike the arithmetic mean, which is sensitive to outliers, the geometric mean gives equal weight to all values and is therefore less affected by extreme values.
- It reflects the true changes in the variable. The geometric mean reflects the compound growth rate of the variable, which is important in many applications. For example, if we want to measure the average growth rate of a portfolio of stocks over several years, the geometric mean is the most appropriate measure.
- It is consistent with the concept of percentage changes. Percentage changes are often used in economic and financial analysis, and the geometric mean is consistent with this concept.

Limitations of G.M.

Despite its advantages, the geometric mean has some limitations:

- It cannot be calculated if any of the values is negative or zero. This can be a problem in some applications, for example, if we want to measure the average inflation rate over several years and there is a year with negative inflation.
- It is difficult to calculate manually. Unlike the arithmetic mean, which is easy to calculate by adding the values and dividing by the number of values, the geometric mean requires taking the nth root of the product of the values.

Use of A.M.

In practice, however, the arithmetic mean is often used in the construction of index numbers for several reasons:

- It is easier to calculate. As mentioned above, the arithmetic mean is easier to calculate than the geometric mean, especially when there are many values.
- It is more familiar. The arithmetic mean is more familiar to most people and easier to interpret. For example, if we say that the average salary in a company is $50,000, most people understand what we mean, whereas if we say that the geometric mean of the salaries is $50,000, many people may not understand.
- It can be used even if some values are negative or zero. Unlike the geometric mean, the arithmetic mean can be calculated even if some values are negative or zero.

Conclusion

In conclusion, while the geometric mean is considered the best average in the construction of index numbers in theory, in practice, the arithmetic mean is often used due to its ease of calculation and familiarity. However, it is important to be aware of the limitations of both averages and choose the appropriate measure based on the specific application.