## 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.