**Definition: **Arithmetic mean is also sometimes called the mean integral of a number sequence, the average of the integral of a set of numbers, or simply the average of a set of numbers. It is the fundamental statistic of statistics: it measures the average contribution in a weighted series of samples during a specified period. The mean is often defined as the average of one value in a series; it is the sum of the deviations from that average over all the values in the series. Mean differs from median and mode in that it is inclusive; that is, it includes the values for which the mean value is less than the corresponding value

In the realm of finance, there is a way to calculate an average based on data that comes from a large number of trials: that is, the arithmetic median. It is a useful tool and has many applications. However, it is often misleading, particularly when applied to small samples or situations with many different outcomes.

The Arithmetic Mean (AM) is one of the most important statistics you should learn. It has a lot of applications in areas like finance, statistics, and probability. It is a statistical measure of the average value of a set of numbers.

**Disadvantages of Arithmetic Mean:**

- When deciding how much to spend on a service or product or how large an investment to make in a startup, the arithmetic mean can be harmful.
- A common misuse of the mean is to compare it with the median or average. While these measurements make sense in average terms (involving the differences between groups), the mean can be misleading when using it on individual data. It’s particularly troubling when comparing means directly
- While the mean can usually be trusted to produce an average across a large population, it’s not always practical to do so. For example, if you have a million customers, the mean will show you 2 million average results per customer. But if there are 10 customers with bad credit and 10 customers with good credit, then the mean will likely show 5
- Averages are good when you have large numbers of observations. If the number of observations is small, it is easy to create artificial spikes that don’t reflect reality.

Apart from AM, other averages used in finance are Geometric mean and Harmonic mean.

The geometric mean is used to summarize the numerical values of a set of data, while the harmonic mean focuses on the relationships between the values. For example, the geometric mean of water temperature at 10 degrees Celsius (50 Fahrenheit) would be 1.0. In contrast, the harmonic mean might give you a score of 3.0, from 2.0 being extremely hot and 6.0 being extremely cold.