©2020, George J. Irwin. All rights reserved.
In this post we’ll discuss the Three Ms of Measurement. I don’t mean 3M here, previously known as the Minnesota Mining and Manufacturing Company, even though they were first with that essential office supply of Lean Six Sigma Practitioners, Post-It® Notes, also known generically as “stickies.”
No, here the three Ms are Mean, Median and Mode. I’ll start off with the least used, the mode, which is the most frequently seen observation in a sample or population. In other words, if you have a data set consisting of 1, 2, 2, 3, 3, 3, 4, 5, and 6, then the mode is three, because it occurs three times in the set, more than any other value. (See, three is a magic number. I just took some of you back to Schoolhouse Rock. Look it up, kids.) By the way, this really only works for values. A mode of “blue” is not terribly useful in my estimation.
The other two measures are far more important. I don’t remember ever having used mode outside of Black Belt Class. Of these two, mean is far more potentially misleading; or as I’ve put it, another word for “average” is “mean,” and “mean” is a four letter word.
Let’s consider the mean, or average, income of the small town of East Overshoe, population 100, which is reported to be $109,900 per year. Wow, that’s really good! How do I apply for membership?
Don’t sign up just yet.
Suppose the fact was that of the 100 people in East Overshoe, 99 of them made $10,000 per year and the 100th person made $10 million. On average, that is the sum of 99 times 10,000 plus another 10 million, then divided by 100. Not so good unless you are that 100th person.
Or what if 99 of the East Overshoers made $25,000 per year and that 100th resident made $8,515,000, not as nice a ring to it as $10 million but not bad. The mean income is still $109,900.
A much better representation of what’s going on in East Overshoe is the median. If you put all of the values in the sample or population in order from smallest to largest, the value that’s bang in the middle is the median. Half of your values are lower and half are higher. Well, not in this case because I made the math easy on us, but you get the idea. The median in the first case is $10,000 and in the second case it’s $25,000. We are able to conveniently, and appropriately, ignore the resident with the big bucks because said resident is not representative of the rest of the town.
I am cheating a bit here because technically, because I have 100 data points which is an even number, the median is between the 50th and 51st data points. I need to take the average of those two—and here it is OK to use the average—but since the two values are identical in both cases, I know that the median is also identical. It’s easy when you make up your own data set.
As we’ll see in other posts, both mean and median have their important places, and it is quite important to know which one to use when. Your Friendly Neighborhood Black Belt can help you with that if need be.