Sunday, April 29, 2012

What's average?

So many reports and articles citing trends just say "average". Yet there are three ways to calculate average and they provide different information, so they have different meanings. 

I wish writers and speakers would offer all three of them: Mean, Median, and Mode. 

Most seem to like the 'mean' average and many like the 'median average. Yet few, if any, like to include the 'mode average' which I consider to be as, if not more, important than the others.

Mean average is calculated by totaling all of the quantities in all of the population groups and dividing by how many people are in all of the population groups. 

Median average simple tells which group's quantity is in the middle, meaning half of the remaining people earn more than that and half of the remaining people earn less than that.

Mode average simply tells you which group's quantity has the most people in that group.

I want to know which quantity has the most of the people. That seems most relevant to me. Of course, I learn even more by knowing all three measures of average.

For example, if 5 people each earn $10,000; 1 person earns $60,000; 3 people each earn $100,000; and 2 people each earn $200,000, then: 
-- Mean average earnings for this group of 10 people equals $73,636
-- Median average earnings for this group of 10 people equals $60,000
-- Mode average earnings for this group of 10 people is $10,000

In the above example, each measure of average paints a different picture. The mode average paints the most different picture. Together they say that some of the people earn a lot more than most of the people, but not so many people earn a lot more.

On a graph, the above would present a curve that has a peak towards the very low income level and then a low, somewhat flat tail towards the high income levels. 

On a graph, a population with an ideally balanced curve is where the most people earn the incomes in the middle. We call that the bell-shaped curve. (Remember that from school?) If we are measuring income, then wouldn't we consider a healthy, wealthy, and happy population to be those with either a bell-shaped curve or a curve with the peak ... the mode ... above the middle?

Seeing that there are different ways to calculate average, that each gives you different information and impression about any population's income distribution and that calculating all of them gives you the fullest picture of the populations. 

Now wouldn't you too want to see the full picture?

So wouldn't you too want to be told all three measures of average by the writer, speaker, economist, politician, and reporter?

Now you know why I told you that I want them to tell me all of the three measures of average?

Numbers only lie when you're not given all of the numbers. But that gets into the differences between "lies of commission" and "lies of omission". You know, when you tell someone something that you know isn't true versus when you don't tell them anything or everything. But that's an issue for another posting. 

Hey, the next time people tells you that you ... or your kid ... is average, ask them what's "average"?

See you next post.

Steve Reichenstein