1.7: Statistics Do Something with Numbers

Part of the problem is that too many numbers are too overwhelming. The other issue is that numbers aren’t exactly bias-free, and we will discuss this in the next section.

There is such a thing as too many numbers. We need to organize our experiences. It follows that we need to organize our numbers. In statistics and life, every time we get overwhelmed with too much “stuff,” we seek to simplify.

We want to understand the temperature of a region, so we use numbers to gather our observations of the temperature, which are based on our experience of “it.” But there are so many numbers generated from different contexts. We take temperature readings in the morning, then in the afternoon, and then in the evening. Then, we take temperature readings when it is raining, snowing, or windy. The temperature readings vary by context. And then there are more contexts. In Chicago, the temperature in the north will differ from the south and in the west, and if you are genuinely from Chicago, you know that temperatures by Lake Michigan are different compared to inland.

All those temperature readings are gathered, and we call them data and put them into a dataset. A dataset is nothing more than a series of numbers based on our observations of variation. When we say “gather the data,” we really mean gather our observations of the “it” in as many ways as possible. By the way, those “ways” are considered the research method, which basically refers to “how you are gathering the data.” As you gathered, we will discuss that issue in more detail.

So, what do we do with this data? We use statistics to do something with the data to achieve a goal. What is that something? There are several somethings: organization, summarize, estimate, predict, and infer. What is that goal? The goal is always this– to understand something.

First, we organize the data, otherwise known as our observations of the variations of “it.” Organization means making sense of something, and using a framework helps. The easiest and simplest framework is to sort something from low to high. We can organize our temperature data from low to high. Sorting from low to high is an intuitive way to manage our experience because we naturally experience “it” from low to high.

Second, we want to take inventory of our “types.” We have temperature as one variable. But if you notice in our temperature example, we have other variables. We have regions: north, south, and west (notice there is no “east side” in Chicago). We have context: rain, snow, wind. We have a unique context: inland or near Lake Michigan in Chicago,” (Google “The Lake and temperature in Chicago” and you will understand the reference). We want to inventory our variables and see how they vary by amount or type.

Third, we want to summarize. No one can process the meaning and the usefulness of a hundred temperature readings. It is efficient to summarize the readings into just one number. We can do much more with just one number. What do we mean by “do much more?”

Fourth, we mean we want to use the numbers for something. That something is usually to make predictions and to understand something.

These four uses for numbers are why we use statistics. These uses are our investigations that form the cornerstone of building our knowledge about what is meaningful.