Motorola claims that its people invented Six Sigma, but the principles behind the methodology date back to 1809. That's when Carl Gauss, a German mathematician, published "Theoria Motus Corporum Arithmeticae." In this book, Gauss introduced the concept of the **bell curve**, a shape that can often represent the variation that occurs in a controlled process.

Before we dive into the statistics of the bell curve, let's talk a moment about **variation**. Variation is defined as deviation from expectation. Every process and activity has inherent variation. If you're making widgets, every widget will vary slightly. If you're swinging a baseball bat, every swing will be different from the swing before it. And if you're signing your name, every signature will contain subtle differences that no other signature will possess. Variation is inevitable and unavoidable. The trick, of course, is to limit it. Some variation is probably OK. Too much leads to the kind of defects we described in the last section.

When data is collected from a typical process and plotted on an x-y axis, the nature of the variation starts to become clear. For example, say you're an employer with an 8 a.m. start time for your business. You want to find out how many employees actually arrive at 8 o'clock. So, you collect the data below:

If you were to plot the data in a bar chart that depicts the frequency of occurrence for each employee start time, you would end up with the chart below. This kind of bar chart is known as a **histogram**.

The histogram provides a visual representation of your variation. Notice that the variation is spread out evenly across a range of values. This is called a **normal distribution**, and the result is a bell-shaped curve. The diagram below shows the same distribution with the bell curve superimposed over it.

Now let's look at a bell curve without any underlying data. Such a curve is shown below so that you can clearly see two important measurements -- the **mean** and the **specification limit**. The mean is the peak of the curve. The specification limit is the value designating acceptable from unacceptable performance. There usually is an upper and lower specification limit for a process -- and the areas on the outside of the limits are called the **tails**.

On the next page we'll talk about standard deviation, which tells us how much variation exists for a given process.