A Case of Two Means:Geometric & Arithmetic

Why is this post there? I have come across several examples of quoting results (numbers) in papers, reports etc. where the authors have used arithmetic mean. For instance, people would run an application on different computing platforms and then calculate the time taken on each platform. They would present their results in a table and the last column would have an entry titled “mean”. Often, it is the arithmetic mean (AM) that is quoted. How many times have you seen the geometric mean (GM) being quoted? Not many. The primary reason being that we are too comfortable with the arithmetic mean. This is what pops up in our heads generally when we think of a mean. But we forget in the process if AM is the right choice. It is important to understand when to use AM and GM . AM is biased towards large data points in a data set while that is not the case with GM. GM is generally used when several quantities multiply together to produce a result while AM is generally used when they add up to produce a result. Sometimes it is obvious when they add up and when they multiply. Sometimes,it is not so obvious. So you have to put extra effort in finding out which mean to use  and what message you are trying to drive home through that mean value. In the example cited in the beginning, GM should be used. Some nice references to read are : ref1, ref2, ref3, ref4. Similary, understanding when to use Harmonic Mean (HM) is also important. Whichever mean you choose,you have to understand your data points as well as be clear about the message you are trying to convey. Means and averages are very important in economics, mathematical finance etc.