Average and Median?

Average and Median values are used all the time, and frankly, if I thought I had some notion of what their respective meaning was, I would have been woefully incapable of giving a simple and clear explanation. 

So, I’ve decided to research that subject here’s what I’ve dug out in the process. If we begin with the definitions, the Average (also called Mean) is obtained by adding up all the numbers in a set, then dividing them by their quantity, for example if our last five test scores are 80, 85, 90, 95, and 100, our average score is: (80+85+90+95+100)÷5=90. 

The Median, on the other hand, is the middle value when the numbers are arranged in order. For the same test scores (80, 85, 90, 95, 100), the Median is 90, because it is the number in the middle of the list. If there's an even number of values, take the average of the two middle ones. The key difference between Average and Median, is how they are affected by outliers (extreme values). The Average is highly sensitive to outliers. A single very high or very low number can drastically pull the average up or down. 

The Median is not affected by outliers. It only cares about the number in the middle, so extreme values at either end do not change it. In fact the visual is the best way to remember which one is which and the difference between the two! The most interesting aspect however is how these measurements can be used and “spun”. Both the average and the median are used to describe a data set, but a person can choose which one to use to influence how the information is perceived. If we look at Average used for spinning information, it’s a great tool for data that’s fairly consistent and doesn't have extreme highs or lows, such as average age of a population or average temperature over a month.

However, because it is sensitive to outliers, the Average can be used to make things look better or worse than they are. For instance, if we want to make things look better, a company with 10 employees, where 9 people make $50,000 and the CEO makes $1 million, could report an "average salary" of over $140,000. This makes it look like everyone is earning a great salary, even though the typical employee makes far less. 

To make things look worse, a labor union leader might report the average salary of a specific group of workers to include some very low outliers, making the overall pay look worse to argue for a raise. When it’s the Median that’s used for spinning information, it’s by far the preferred tool for data sets that have extreme outliers, like income or housing prices. It gives a much more accurate picture of what a "typical" value is for that group. To that effect, the Median is often used to counteract the "spin" of the Average. 

A journalist, for example, would report the median income to show what a typical family earns, as it is a more honest representation. However, it can also be used in its own way, like if a community is very wealthy but has a few very poor residents, a report focused on the "median income" might understate the overall wealth and resources of the community as a whole. 

In summary, a company might say, “Our Average salary is $120,000,” but if a few execs earn millions, the Median might be only $65,000 — a more accurate picture of what most employees earn. Politicians might cite Average income to show growth, while critics use Median income to highlight stagnation for the majority. So depending on the story someone wants to tell, they’ll choose the measure that best supports their narrative. It’s a classic case of “truthful but misleading”, so watch out next time you see Average and Median, remember the true meaning of both!