Arithmetic Mean

The arithmetic mean refers to the easiest and most common measure of an average. In other words, it includes dividing the received sum by a number of units in a row. For instance, consider the following numbers: 39, 47, 63 and 89. The total sum equals to 238. So that the arithmetic mean is 59.5.

Of course, there exist other types of means, implying geometric and harmonic ones. These measures become effective in certain situations concerning finance and investments. Another case presupposes a trimmed mean, employed to calculate economic data, including the CPI and PCE. 

Essence of the term

Financial analysts and portfolio managers often need a single number that is representative of the likely decision outcome. That’s where the arithmetic mean comes into play for estimating a data center. 

Let’s suppose a person is willing to calculate an expected return for 18 analysts engaged in particular stocks. In order to do this, all the estimates are summed up, and then are divided by their number, which is 18. So that the resulting figure signifies the arithmetic mean. Only math skills are needed.

In fact, the arithmetic mean assists in describing a digital value set with exclusively one number. Using the above formula, there is a possibility to calculate the average price for a product, or the average salary of employees in the enterprise. This is useful for keeping statistics, along with cases of succinctly presenting data.

Usage limits

If a person multiplies numbers instead of adding them up, they should use the geometric mean instead of the arithmetic one. The most common example is when calculating the return on financial investments.

For instance, if the stock fell by 10% during the first year, and subsequently rose by 30% during the second, then it is incorrect to seek for the "average" increase over this period as the arithmetic mean would be: (-10% + 30%) / 2 = 10%; the correct average, there, is the compound annual growth rate, which gives an annual increase of only 8.2%. 

Therefore, the arithmetic mean doesn’t work well for estimating performance of investment portfolios. Alternatively, it isn’t the case to make portfolio performance overviews, when the idea touches upon compounding, or reinvested dividends and profits. Moreover, this technique cannot be applied to account current and prospective cash flows, as it may result in misleading figures. 

Note: the arithmetic mean is able to cause deceptive outputs if there are outliers, or historical profitability is taken into account. Therefore, the concept is more suitable for sets that show serial correlation. 

Comparing arithmetic and geometric means

As a matter of fact, the geometric mean is most commonly used to calculate the average of growth rates, returns, etc. In the financial sector, the term implies receiving average growth rates of profits, revenues, returns on funds and other indicators.

It is believed that the geometric one is better suited to describe past returns, while the arithmetic mean is more compatible to estimate prospective earnings. Thus, the first concept summarizes an income of past periods through compound interest, and the second gives an idea of the income for one period without complex returns.

In practice, the geometric average is below the arithmetic one. In case a difference between them is greater, the greater would be a variability of observations for time intervals.