Several years ago, in the essay Average is the Enemy, I wrote about the “false shortcuts offered by averages” for making decisions. Averages give a sense for where the middle lies within a group. They offer a starting point for understanding a situation but, like stereotypes, are incomplete and can mislead.
Mathematically, averages specify the arithmetic mean. Calculating an average represents one of many approaches for profiling data when conducting analysis. In fact, averages themselves come in different forms. When conducting forest industry research, my team at Forisk often uses rolling and weighted averages to address different issues and better leverage underlying data.
Rolling Averages
A rolling, or “moving,” average provides a way to measure trends over time. This can be useful when studying the status of a situation from daily, weekly, or monthly data, such as housing starts, health trends, and the economics of different businesses. For example, in the forest industry, the COVID-19 pandemic initiated two years of extreme volatility with softwood lumber prices. Indexed monthly prices increased 71% in mid-2020 before resetting and spiking to an all-time high in mid-2021 and resetting and cycling steeply again in 2022 before, relatively speaking, stabilizing.
When evaluating product margins over time, we want to avoid over-exposure to outliers or random spot prices, such as when lumber exceeded $1,500 per thousand board feet (MBF) in mid-2021. A rolling average cuts a path through the cycle to “smooth out” reported prices while still including the most recent data. In this way, we might apply the last three, six or twelve-month average lumber price to fairly assess the break-even and potential profitability of a business or sector.
Overall, a rolling average provides a practical way to readily communicate insights from simple data series. The Economist calls them, “Among the unsung heroes of statistical methods…” I agree.
Weighted Averages
A weighted average accounts for the relative importance of certain aspects of the data. This differs from a simple average, which treats all observations in a data set equally. In this way, and depending on the question asked, a weighted average can improve our use of available data.
Consider another forest industry example. In 2022 in the U.S. South, the four-quarter rolling average price of pine sawtimber, the logs bought by sawmills to produce the softwood lumber used for homebuilding, was $27.79 per ton according to data from TimberMart-South. This number is a simple average of 11 state-level prices, from Texas to Virginia and down to Florida. However, when we weight those prices by log use (volume) by state, we get $28.59 per ton.
The difference reflects how higher volume states with more sawmills and higher lumber production levels reported higher log prices and vice versa. For example, Georgia, with a 2022 average price of $33.43, consumed around 13 million tons of pine sawtimber in 2022, while Virginia reported a price of $21.17 while using around 3 million tons of sawtimber over the same period.
We can also combine approaches to calculate a rolling weighted average. This will better reflect the state of the sawtimber market and the value of wood delivered regionally over time.
Conclusion
Systematic exploration of a situation benefits greatly from the proper, context-appropriate application of available tools and methods. The calculation of an average is, of itself, an agnostic act. However, its ability to clarify depends on the underlying data and question being asked. Rolling and weighted averages, and their combination, offer ways to improve our understanding of a given situation.