Geometric mean of 2 and 20 investing

The geometric mean is used in finance to find the average growth rates which are also known as the compounded annual growth rate CAGR. Geometric Mean is also used in biological studies like cell division and bacterial growth rate etc.

M are as follows: The G. If each value in the data set is substituted by the G. M, then the product of the values remains unchanged. The ratio of the corresponding observations of the G. M in two series is equal to the ratio of their geometric means. Geometric Mean vs. Harmonic Mean While the geometric mean tends to be better suited to find central tendency in a set of values with a multiplicative relationship, the harmonic mean is more effective when the set contains values that are ratios.

Harmonic Mean To exhibit the varying effectiveness of geometric mean vs. An object travels from one point to another covering a distance of km. The harmonic mean calculated above shows an average velocity of If the object traveled at that velocity for the same 6 hours, it would travel exactly km.

This same distance our object traveled in this scenario at its varying velocities. The geometric mean calculated above shows an average velocity of If the object traveled at that velocity for the same 6 hours, it would travel roughly km - a distance that is 68km further than our object actually traveled.

Therefore, in this scenario, the geometric mean yields an average velocity that is less meaningful than that yielded by the harmonic mean. Applications of Geometric Mean The geometric mean has many applications in many different fields including medicine, finance, computer science, and elsewhere.

Medicine - Understanding Growth Rates using the Geometric Mean In science and medicine, the geometric mean is used to understand statistical rates of growth. This growth can be human population growth or the growth of a bacteria or virus, or even of biological processes such as gene expression, a normal process which occurs in the cells of all living organisms. In such cases, the geometric mean, rather than the arithmetic mean, is relevant. For an example of how the geometric mean is used in understanding growth rates, consider the following example of bacterial growth.

You are a cancer researcher working in a lab and are trying to grow a batch of Chinese Hamster Ovary CHO cells in the lab to examine the effects of different anticancer compounds on these cells. You only have a few cells, and have to wait for them to multiply so you can do your different experiments. You start off with CHO cells. This is your first time growing CHO cells, so you decide to calculate the growth rate so that you can be able to grow the right amount of cells easily next time you need more CHO cells.

Geometric means work here to help you calculate the growth rate because cell growth is a nonlinear process, so arithmetic means would not be helpful. This number makes sense because the doubling time of CHO cells is about hours. The resulting total number of cells at a constant growth rate equal to our geometric mean matches the the total number of cells in the original scenario outlined.

Knowing the average growth rate found using the geometric can be used to estimate how long cells should be grown in another experiment to achieve a desired total number of cells. Finance - Calculating Investment Returns Using the Geometric Mean In finance, geometric mean is used to calculate the rates of annual growth of an asset. The compounded annual growth rate CAGR is the same as the geometric mean of the growth of an asset over time.

CAGR can be used to track the growth of a stock over several years.

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