We have to aim for something. In most applications, we have a general idea that we are going to “hit” somewhere near our target. This is good.

But what if you miss?

What will you hit if you miss?

Let’s say your target is 6, and your “bullets” are the product of two dice.

So in order to get 6, you could have 2&3 or 3&2 or 6&1 or 1&6.  That’s four different ways to “hit the target.”

What will you hit if you miss? Will you hit 7? Will you hit 5? Those are the two numbers in closest proximity to 6. How likely are each of these outcomes?

What’s the average of this distribution of dice products?

Our intuition fails us.

This distribution has its basis in an odd assortment of numbers between 1 and 36, but not all of them.  And as we just pointed out, 7 is not one of the possible outcomes.

So if we missed six, we have no reason to think that we would “hit” nearby.

It’s okay to use the average, as long as we know what we will hit if we miss.

When we drive down the road, we don’t need to stay in the middle of our lane, but we have a good understanding of where the edges are.

We need to understand more about the underlying distribution–whether it’s an estimate of revenue in business plan, flight test data, or safety statistics.

You aren’t average. Life isn’t average. That’s why average isn’t good enough.

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Where Do We Go From Here

How do we find our way then, when we are exploring the unknown, blazing a trail into uncharted territory? How do we apply elementary statistical principles to transform uncertainty into decisive action? What is to prevent us from making a preposterous application of ATOMs when we deal with very complex situations, those in which our intuition fails?

These questions are not much different from those faced by Chuck Yeager before he ever broke the sound barrier or Neil Armstrong as he took that first step on the moon. Neither of these men, nor anyone around them–with hundreds or thousands of highly educated, very scientific people on these teams–knew what to expect. Or did they…?

ATOMs is a monthly column that introduces analytical tools of mathematics and statistics and illustrates their application. To read more about ATOMs, you can read Where Do We Go From Here, or view the online workbook here.