After measuring the properties of individual stars, how do astronomers use this information to classify them? Classification can be a key to physical understanding. Classification is the act of gathering data, looking for common traits and features, comparing like with like, and trying to make sense of the patterns. It may sound more exciting to invent a new theory than to classify phenomena in the natural world. Classification can be mundane, but in the hands of an expert, it is an art. This kind of work led to the realization that the Earth and the species that inhabit it evolve. Classification was also the key to demonstrating that stars evolve.
To review a simple example of classification, think of motorized vehicles plotted in terms of their weight and engine power. The sequence of cars increases in weight and power, running from compact to mid-size and on to luxury cars. There are also special categories, such as trucks, which have a lot of power for their large weight, and sports cars, which have a lot of power for their modest weight. You would not find every combination of weight and power. Any vehicle with a small engine that was very heavy would be too under-powered to be useful! Classification and measurement teaches us something about the power demands of vehicles.
Here is example that is analogous to classifying stars. Imagine that you live in a small town. You gather information on each of the inhabitants: their age, height and weight. A graph of everyone's height and weight would show a clear and obvious trend. People spend most of their lives as adults, so most measurements show adults of average height and average weight. There would be a tail of measurements showing children of younger and younger ages. A line drawn through the data would show the average characteristics of people as they age. This line reverses itself; old people actually shrink. There would also be unusual groups of people whose combination of height and weight did not match most people: those that are very tall (members of the high school basketball or volleyball team, perhaps) and people with congenital conditions that retard growth.
There are two important points to note. First, humans cannot be found with any combination of height and weight. You will never see someone who is 3 feet tall and 300 pounds, or 6 feet tall and 60 pounds! The pattern of occurrence of heights and weights tells us something about the shape of the human organism. Also, the location of an individual on this plot is primarily fixed by age. In other words, although we have plotted height against weight, the hidden variable is time. As humans age, they grow so that their measurements will shift on a graph like this.
What if intelligent aliens visited a small town on a fact-finding mission? The aliens would notice small and large people, and they might notice a trend in the plot of height against weight. But could they deduce from a quick visit that the small (young) turned into the large (old)? Astronomers are faced with the same situation in unraveling the life stories of stars. We get a snapshot of stellar properties and must deduce how and why they change over time. Luckily, there is a powerful method of classifying stars, a method that has revealed important information about nearby stars, prominent stars, and stars of very different sizes.