Did you know there are different types of averages? Averages are not limited to just the familiar arithmetic mean we encounter in everyday life. In fact, various types of averages, such as geometric mean, harmonic mean, serve unique purposes in business settings. These averages provide powerful tools for analyzing data, evaluating trends, and making informed decisions. In this article, we will delve into the different types of averages and explore how they are applied in business settings.
- Arithmetic Mean:
Let’s start with something basic. The arithmetic mean (the official name), often referred to as the average, is the most commonly used measure of central tendency. It is calculated by summing up all values in a dataset and dividing the sum by the total number of observations. It provides an overall snapshot of performance and helps identify trends over time. When we create measures like “average weekly sales”, this is the average that we are referring to.
Example: Suppose you have a dataset of weekly sales figures for a retail store: $10,000, $12,000, $15,000, $9,000, $11,000.
To find the arithmetic mean (average) of these sales figures, you sum up the values and divide by the total number of observations: ($10,000 + $12,000 + $15,000 + $9,000 + $11,000) / 5 = $11,400.
Therefore, the arithmetic mean of the sales figures is $11,400.
Now we have covered the basics, let’s explore other types of “averages”.
Geometric Mean
The geometric mean is a type of average that is particularly useful for analyzing growth rates, compound interest, investment returns, and other situations involving multiplicative factors. It is calculated by taking the nth root of the product of n values. The geometric mean is beneficial in business when analyzing performance over multiple periods or evaluating the average growth rate of investments or market indices.
where:
R₁…Rₙ are the rates of interest (or other observations for averaging).
Example: Consider a scenario where you want to calculate the average annual growth rate of an investment over a 3-year period. The annual returns are as follows:
Year 1: 10%
Year 2: 5%
Year 3: 8%
To find the geometric mean, you multiply the annual returns and then take the cube root (since we have three years):
Geometric mean = (1.10 * 1.05 * 1.08)^(1/3) — 1 = 7.58%.
Therefore, the geometric mean annual growth rate of the investment over the 3-year period is 7.58%.
If you simply added the numbers and divided by 3, you’d get 7.67%. This error seems small, but in financial, if you are estimating average returns over several years, this error is too big to ignore.
Harmonic Mean:
The harmonic mean is primarily used when dealing with rates, ratios, and average rates of change. It is calculated by dividing the total number of observations by the sum of the reciprocals of those observations. In business, the harmonic mean is commonly applied in various fields, such as finance and operations, to calculate average rates, average speeds, or average costs. For instance, it can be used to determine the average cost per unit produced or the average rate of manufacturing at a factory.
Example: Imagine you want to calculate the average rate of manufacturing between 3 factories:
Factory 1: makes 50 widgets per hour
Factory 2: makes 60 widgets per hour
Factory 3: makes 70 widgets per hour
To find the harmonic mean, you divide the total number of factories by the sum of the reciprocals of the rate: Harmonic mean = 3 / [(1/50) + (1/60) + (1/70)] = 58.97 widgets per hour.
If you calculated a simple arithmetic mean, you would have arrived at 60 and introduced some error.
Conclusion:
Averages are indispensable tools in business analysis, offering valuable insights into performance, growth rates, trends, and decision-making. Understanding the different types of averages, such as arithmetic mean, geometric mean, harmonic mean, enables businesses to leverage these measures effectively. By applying the appropriate average to the specific context, you will get a much more accurate result or estimate.