by Jacqueline Verrilli
I believe that the formula above holds
the answer to all of life’s problems. This
humble little formula is the most common of all formulas in mathematics and is actively
used in every human endeavor of every kind in any discipline. It is deceptively simple in nature, involving
only addition and division to derive, and yet within this simplicity is a
powerful beauty beyond any that can be achieved in painting, sculpture, or
literature. It has most certainly been
around since shortly after we started counting things and so it shocks me that
no one, outside of statisticians, has revered it or even so much as paid much
attention to it. I believe that it is
the equation for life, the universe, and everything and I’m sorry that Douglas
Adams won’t get a chance to read my blog, but hopefully the inter-dimensional
beings are reading it now and will make this formula their new Supreme Being.
For those of you that haven’t used
mathematical symbology since high-school or college (or ever), the weird
looking set of hieroglyphs above is just the formula to calculate the average
of a bunch of numbers, also known as the arithmetic mean. Like most math, the calculations behind this
scary-looking equation are actually relatively easy to do. For example, the mean of the numbers 13, 5,
17, 22, and 20 is 15.4 and is simply calculated by adding the numbers up and
dividing the total by the number of numbers.
If you had, say, a bunch of bushels of oranges, you could count the
number of oranges in each bushel and find the average number of oranges per
bushel. And if you did this, as long as,
the bushels were not filled by a super-accurate machine that put exactly the
same number of oranges in each one, you would find that the number of oranges
in each bushel varied a bit, so that there would be a distribution of numbers
around the mean number of oranges per bushel.
Below is a graph of a distribution
of numbers around a hypothetical mean.
This is a very typical graph that is often described as a bell-curve,
for obvious reasons, but is known among the mathematically–minded as a “normal”
distribution. The conventional
interpretation for bell-shaped distributions is that we tend to think of the
right side as positive (or higher or “better”) and the left side as negative
(or lower or “worse”). I took this
particular version of a normal distribution off of the internet and, as you can
see, whoever created it was using it to show some distribution of
“ability”. We can think of this ability
as just about anything. We could, for
example, make everyone in the world perform a standing jump, measure the height
of each person’s jump and we would likely see a normal distribution across the
population. Most people would be able to
jump, say, 18 inches off the ground, others would only be able to jump 8 inches,
while other could jump 25 inches. At the
very extreme ends we might see a few souls who were able to jump, say 33
inches. These people might fall into the
tail of the bell curve on the right-hand side which would mean that they fall
above 99% of the rest of the population in ability to jump high from a standing
positon. These would likely be your
Olympians if you could find them in your country. Others may only be able to jump, say ¼ of an
inch. These folks would fall into the
tail on the left side of this distribution falling below 99% of the population
in this particular ability. Normal
distributions occur around the mean, or average, of the population’s “ability”,
so those of us who fall in the middle, jumping 18 inches, would fall on the
line in the very center. Let’s say ½
billion of us fall at exactly 18 inches, then the people who could jump 17.95
inches would fall just to the left of us, and the people who could jump 18.05
inches would be on a line just to the right of us. So you can, hopefully, now see that this
graph also shows the relative number of people (or things) that would fall into
each level of the measurement. That is
why this is also called a density distribution function.
Average is the New Awesome
Let’s look at a bell curve for “success”. In point of fact, the definition of success is as subjective as all-get-out, but since this is an economics blog, let’s just use "wildly wealthy" as our definition of success. The media LOVES to cover the lives of wildly wealthy people. So we hear about them, ad nauseum. We don’t often hear about people who are huge successes at just being decent human beings. Our sample of "successful people" is, therefore, generally comprised of those who are in the tail ends of the bell curves, which are subject to availability bias. For example, we might consider Warren Buffet or one of the Kardashians one of our success heroes. But we, as consumers of the media, we, the
average people, make up the market for information. And if we stopped caring about those people in the
tail ends of the “success” or “fame” bell curves and started watching only
stories about average people, the media would have to respond in kind. We simply don’t understand the power that we
have in that opportunity! My Econ Prof
even pointed out the power that the average person has over the distribution of
money. Each time we click on an ad that
has been placed with Google, Google gets money! Can’t you feel that rush of power! Imagine if we could just get rid of the
Electoral College! The point is, it is those
of us in the tall and wide part of the bell-curve that have all the power. We
are the vast majority of the “normal” in Normal Distribution, after all. And it behooves us to use that power in the most
efficient and effective manner because, as we all know, with great power comes
great responsibility. That’s why average is the new awesome!
Everybody Please Hold Hands and Take One Step to the Right
It is the average person that makes the world go ‘round, not
the outliers. The average person
determines who wins an election, what prices prevail in markets, which goods
and services are provided, and what team gets the good odds in Vegas. We can argue that the monied and powerful people
manipulate the systems and, yes, this is true, because we average people allow
it. We allow ourselves to be bought and manipulated
and then place the blame outside ourselves.
It is an evolutionarily ingrained instinct to think of ourselves as
autonomous and above influence, all the while allowing the outside world to effect
our self-image, and our self-confidence, and, hence, our autonomy. As much as we want to be viewed as special by
everyone else, we are built to fit it so that we can be accepted and belong and
enjoy the protection of the group.
But
when even one of us does something that is a little different, even when we
think we are doing it just for ourselves, like, say, sitting in the front of
the bus, or wearing pants suits on the Congressional floor, or starting an
internet search engine to help us find what we want more easily, the world
actually gets better for everyone. When
a writer writes a great story, or an engineer designs a mechanical solution, or
a teacher finds a way to help students understand chemistry, or a doctor describes
a new illness, they feel proud of themselves because solving problems is fun. And if one person improves their own
well-being, it improves all well-being. And
you don’t even need to invent or discover anything to improve your own well-being
or that of anyone else. When my garbage haulers
just do their jobs, it makes my life a WHOLE lot better because I don’t have to
do anything other than drag the can to the curb! When someone else teaches my children
biology, I don’t have to; when someone drives a truck that delivers broccoli to
my local grocer, I don’t have to; and when my husband takes the no-kill mouse
trap out to the back yard, I don’t have to. I would argue that they, thereby, improve my well-being. Now, according to the calculation of a mean, if
even one person under our bell-curve becomes better-off in terms of their
well-being, it moves the entire mean to the right. This shift may be ever so slight; so
incredibly slight as to be unnoticeable to the casual observer, but the mean,
nevertheless, has moved, and we can calculate the amount of the change.
Sure, But What's in it for Me?
I hope you’re as excited as I am at this
point because here’s the BEST PART! Remember
that formula for the mean and how you add up all the numbers before you divide? That’s why I believe that the mean is the
math to enlightenment: it is an axiomatically logical and mathematically
calculable function of what many people know to be true intuitively; that we
are all interconnected to one another.
Our actions affect one another without us even necessarily meaning for
it to happen!!!! And wait!! It gets even BETTER because of what that means
to society as a whole. It is
everyone’s purpose in life to move the mean to the right. And we all do it just be being ourselves! Just imagine if we all started to actively
help one another out!! Holy compassionate
actions, Batman!
Red Shift
When one person who might have dropped out of school instead
stays in and completes a high school diploma or a college degree, the whole
world is better off. If a teacher or
mentor helped to influence that outcome the whole world is even better off. If even one person helps someone, anyone, that
is even just slightly to the left of them on the bell-curve in any ability and
that individual goes on to use this newly improved ability to their advantage,
the mean for the world’s well-being moves to the right. The graphic above is the latest assessment of
an agglomeration of factors contributing to Subjective Well-being as reported via
a survey given to the peoples of countries around the globe. It is from a document quaintly entitled the “The
World Happiness Report 2015”. If you’ve
heard anybody state recently that Switzerland is the “happiest” country in the
world it’s because of the data contained in this report. Don’t let the cutesy title fool you, though,
the report is 87 pages long, involved the collection of thousands of data
points, and involved statistical analysis of those points. All to arrive at a mean level of well-being
for each country, and that mean is then categorized and color-coded. As is convention, red is worse than green. I sincerely hope that everyone will read “The
World Happiness Report 2015”. It is an
important document for individuals as well as world leaders and social
scientists. But even if you don’t read
it, take a huge deep breath and go to work or send your kids off to school
knowing that any little positive thing you do helps us shift away from the
red. And “The World Happiness Report” will
thank you.
http://worldhappiness.report/ed/2015/
http://worldhappiness.report/ed/2015/
Helliwell, John F., Richard
Layard, and Jeffrey Sachs, eds. 2015. World Happiness Report 2015.
New York: Sustainable Development Solutions Network.
New York: Sustainable Development Solutions Network.