Arithmetic Average Has Strengths and Weaknesses
Arithmetic average is the most popular measure of central tendency and (the reason for its popularity is that) it is the easiest one to calculate. However, like every other statistical measure, arithmetic average has strengths and weaknesses and it is more suitable in some situations than in others. The following is a summary of situations when using arithmetic average is appropriate and those when arithmetic average should be replaced or complemented by other measures.
When to Use Arithmetic Average
- When you work with independent data, for example performance of multiple stocks or investments in a single period of time (otherwise geometric average may be better).
- When all items in the data set are equally important (otherwise use weighted average).
- When you need a quick, easy, and rough information about the overall level. Arithmetic average is the easiest one to calculate.
- When you don’t have a computer at hand. Arithmetic average is much easier to calculate in your head or on paper compared to geometric, harmonic, or weighted average.
When Not to Use Arithmetic Average (Alone)
- When the data set contains extreme values. Extreme values can bias arithmetic average to value which is not representative of the real central tendency in a data set. Median addresses this issue better.
- When errors can be expected in the input data. Sometimes you can have errors or missing data in your data set. For example when you download stock market data from a trading platform, some pieces of data can be missing. Some programs automatically set price or performance of a missing item to zero, which could taint your arithmetic average calculation. Before using arithmetic average (or any statistical tool), make sure your inputs are correct.
- When data set is very volatile or dispersed. There is nothing wrong with using arithmetic average for dispersed data sets. In fact, replacing arithmetic average with some other measure like geometric average will not solve all your problems here. It is always a good idea to add other statistical measures to your analysis to check the volatility or skewness in the data set (arithmetic average and other measures of central tendency can’t identify and describe such characteristics).
- When you work with percentage returns over multiple time periods, especially when the returns are volatile. In this case, the basis for the percentages is very likely to differ significantly from period to period and arithmetic average is quite useless. Geometric average is better here. See reasons and example here: Why arithmetic average fails to measure average percentage returns over time.
- When individual items have different weights or different importance in the data set. Arithmetic average assigns equal weight to all items. When you need to reflect different weights (for example in a portfolio of stocks or a stock index), weighted average is more useful. See reasons and example here: Why you need weighted average for calculating total portfolio return.
Getting a More Complete Picture
In many cases it helps to use arithmetic average together with other measures, such as median or standard deviation. You can easily calculate these and other statistics in Excel using the Descriptive Statistics Calculator.