60 Questions

What is Central Tendency?

The central tendency is stated as the statistical measure that represents the single value of the entire distribution or a dataset. It aims to provide an accurate description of the entire data in the distribution.

The central tendency of the dataset can be found out using the three important measures namely mean, median and mode.

What is Geometric Mean?

The geometric mean is a measure of central tendency that is used to find the average of a set of numbers, especially when those numbers are products of each other.

$$ GM = \sqrt[n]{x_1 \cdot x_2 \cdot \ldots \cdot x_n} $$

or another form of writing this equation is

$$ GM = \text{Antilog}\left(\frac{1}{n} \sum \log(x_i)\right)

$$

Some of the important properties of the G.M are:

• The G.M for the given data set is always less than the arithmetic mean for the data set
• If each object in the data set is substituted by the G.M, then the product of the objects remains unchanged.
• The ratio of the corresponding observations of the G.M in two series is equal to the ratio of their geometric means
• The products of the corresponding items of the G.M in two series are equal to the product of their geometric mean.

Applications of GM😑

• It is used in stock indexes. Because many of the value line indexes which is used by financial departments use G.M.
• It is used to calculate the annual return on the portfolio.
• It is used in finance to find the average growth rates which are also referred to the compounded annual growth rate.