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# Arithmetic Mean: Definition, Limitations, and Alternatives

Photo: Arithmetic Mean Photo: Arithmetic Mean

How Does Arithmetic Mean?

The arithmetic mean is the simplest and most popular way to measure a mean or average. It simply entails adding up a collection of numbers and dividing that total by the total number of numbers in the series. Take the digits 34, 44, 56, and 78 as an illustration. It comes to 212. 53 is the arithmetic mean, or 212 divided by 4.

Other methods, such as the geometric and harmonic mean, are also employed, which are relevant in some financial and investment contexts. Another illustration is The trimmed mean used to calculate economic statistics like the consumer price index (CPI) and personal consumption expenditures (PCE).

How Arithmetic Means Operate

The mathematical mean continues to be used in finance. For instance, arithmetic means are frequently used to estimate mean wages. Let’s say you’re interested in learning what the 16 analysts who cover a specific stock predict for profits on average. To find the arithmetic mean, add all the estimations and divide by 16.

The same applies if you’re attempting to determine a stock’s average closing price for a specific month. Let’s say that a month has 23 trading days. To find the arithmetic mean, add up all the costs, divide by 23, and you have your answer.

Most people with a basic understanding of business and mathematics can compute the arithmetic mean since it is so straightforward. Due to its propensity to produce relevant findings even with vast groups of numbers, it is also a valuable measure of central tendency.

The Arithmetic Mean’s Limits

The arithmetic mean isn’t always the best choice, especially when one outlier might significantly distort the mean. Say you wish to calculate the allowance for a class of ten children. Nine of them receive weekly allowances ranging from \$10 to \$12. The tenth child receives a \$60 allowance. The arithmetic mean will be \$16 because of that one outlier. This doesn’t reflect the group very well.

The median allowance of 10 could be preferable in this situation.

Additionally, the arithmetic mean performs poorly in estimating the performance of investment portfolios, particularly when compounding or dividend and profit reinvestment are included. Additionally, it is typically not utilized to determine the present and upcoming cash flows that analysts use to estimate. It is nearly certain that doing so will provide false data.

Geometric Mean vs. Arithmetic Mean

Analysts frequently utilize the geometric mean, computed differently, for these purposes. The geometric mean is the most suitable choice for series with serial correlation. Portfolios of investments are one exception to this rule.

Most financial returns are connected, including bond yields, stock returns, and market risk premiums. Compounding and using the geometric mean become increasingly important as the time horizon increases. By accounting for year-over-year compounding, the geometric average gives a far more precise calculation of the underlying return for volatile values.

The geometric mean increases the sum of all the series’ numbers to the inverse of the series’ length. By hand, it is more time-consuming. However, Microsoft Excel’s GEOMEAN tool makes it simple to compute. The geometric mean is computed differently from the arithmetic average or arithmetic mean because it considers compounding that takes place over time. Investors typically believe that the geometric mean is more accurate to estimate returns than the arithmetic mean.

Example of Geometric Mean vs. Arithmetic Mean

Suppose a stock has returned 20%, 6%, 10%, 1%, and 6% during the past five years. The arithmetic mean would add those together and divide by five, resulting in an average return of 4.2% annually.

Instead, (1.2 x 1.06 x 0.9 x 0.99 x 1.06)1/5 -1 = 3.74% each year would be used to obtain the geometric mean. It should be noted that the geometric mean, which is a more accurate computation in this instance, will always be lower than the arithmetic mean.

Conclusion

• The sum of a series of integers divided by the count of that series of numbers is the simple average, the same as the arithmetic mean.
• The arithmetic mean is typically not a good way to calculate an average in finance, especially when one outlier can significantly affect the average.
• The geometric and harmonic means are two more averages that are more frequently employed in finance.