The measure that rules us all
You fell under its charm, finding comfort on it, more than once. And it’s OK. But, I’m here to tell you that you can do better.
It’s 9 pm on a Saturday. You are going to meet your friends at the restaurant. Marc texted you to check at what time you are going to be there.
You take out your phone, open the map app and look for the address. It will take you 20 minutes to get there.
The receptionist at the restaurant tells you that your table is still occupied. That you will have to wait 15 minutes for it to be ready.
What is the secret behind this? Does your app control the traffic? The receptionist will kindly force the other clients to pay and leave? There is some kind of black magic behind all this?
Nope.
Some call it experience. But deep down its just averages … or Mean, to be more precise.
The app knows how much time it took others to make that route. The restaurant knows how much time clients stay on the table. By having this data, they calculate the Mean and give it to you.
The truth behind the success of the Mean
From all the math concepts we learn, the Mean is, by far, one of the most popular and acclaimed ones.
But, why?
Well, it gives us certainty. And with it, comfort.
Our brains like concrete things. They don’t like that you go stressing them out with possibilities and stuff. They want you to go right to the point.
Having to decide is stressful. If you have Netflix and you are the one responsible to pick the show/movie, you know what I'm talking about.
When there are too many options, we tend to suffer. Averages give us the possibility to have one single answer.
“I’m gonna be there in 20 minutes.”
But that’s not all. When we are choosing, we want to be right.
Let's imagine this: You agreed with your friend that you were going to give each other a Christmas gift this year. It has to be something between 20 and 50 bucks.
You are worried to pick a 20$ gift and seem cheap. But spending 50$ its too much (also Marc will not buy you a 50$ gift, cuz you know … it’s Marc).
So, what do you do?
That’s when the 35$ gift appears. BAM! Right in the middle. It’s not too low, it’s not too high. It’s -average- perfect.
Thank you, Mean! You saved the day.
The mean side of the Mean (pun intended)
But, where is the catch?
Well … If it were for averages, a human being has 1 testicle and 1 boob.
Let's imagine that you are looking to move to a new city, you do your research ending up with 2 candidates:
- Awesomeville. Mean salary: 50k/year
- Trapville. Mean salary: 50k/year
So, with this information, it seems that it does not matter which one you pick. Even with the name of one of the cities against itself, there is no clear reason to pick one or the other.
As you don't feel comfortable making the decision yet, you get in touch with a couple of people from each city. You all do the same and they are happy to help and share their incomes with you. This is what you find out:
- Awesomeville. Salary 1: 49k/year. Salary 2: 51k/year.
- Trapville. Salary 1: 20k/year. Salary 2: 80k/year.
They are quite different now, aren’t they?
So what happened? Your first info is correct. The Mean salary for each city is exactly the same.
The Mean doesn’t tell you how dispersed the values are. It points out where the middle between them is. It doesn’t take into account how dispersed they are.
This variability is measured by the Variance (easily calculated on any spreadsheet tool).
- Awesomeville. Variance: 2
- Trapville. Variance: 1800
A high Variance will imply that the values are farther from the Mean, a low one, the opposite.
Depending on what kind of decision you are taking, this Variance is a key factor that you need to take into account.
In the end, this will not give you the right answer. There is no right or wrong based on these calculations. But it helps you take better decisions based on your needs.
If you have no financial compromises, you might pick Trapville for the chance of hitting that 80k job. But if you have a loan that requires a salary of around 50k/year, well … my recommendation is that you move to Awesomeville instead.
Remember when you used your phone to check how long it would take you to get to the restaurant?
Have you noticed that sometimes, your map app gives you a range of values, not a single one? When there is too much Variance, they know that the Mean is not enough. In these cases, a range of values is given to you instead.
This is not all, folks
I don’t want you to think that now, the right thing to do is to use the Mean combined with the Variance as a magic bullet.
NOT AT ALL.
This is the tip of the iceberg. There are many tools that will help you do a more in-depth analysis. For example:
- If you find that the Variance is hard to digest, you can use the Standard Deviation, instead. It will give you a more understandable value.
- If you want to know the probability of a value being too far away (above or below) the Mean, you can use the Skewness.
Ok, enough of terms and concepts and wordy things. I want to give you an idea of how many tools are out there to help you make better decisions.
They will not tell you what to do. They will present you the information so you can decide. You don’t have to use them all, nor all the time. It will depend.
Being 5 minutes late for your dinner it’s not a big deal. Gaining 50k a year instead of 80k, might be.
Be aware that you can have much more than just the Mean.
Today it is easier to find data than it was 20 years ago. We have to use the right tools to get the most out of it.