Probability and Statistics for Finance

Chapter 3. Measures of Location and Spread

Now that we have the data at our disposal, maybe classified, and possibly the corresponding frequency distributions computed as well, it is time to retrieve the information using some concise measures. Generally, there are two possible ways to do this. In this chapter, one of the two ways is presented: the computation of key numbers conveying specific information about the data. The alternative, the graphical representation, will be presented in the next chapter. As key numbers we will introduce measures for the center and location of the data as well as measures for the spread of the data.

Parameters vs. Statistics

Before we go further, however, we have to introduce a distinction that is valid for any type of data. We have to be aware of whether we are analyzing the entire population or just a sample from that population. The key numbers when dealing with populations are called parameters while we refer to statistics when we observe only a sample. Parameters are commonly denoted by Greek letters while statistics are usually assigned Roman letters.

The difference between these two measures is that parameters are values valid for the entire population or universe of data and, hence, remain constant throughout whereas statistics may vary with every different sample even though they each are selected from the very same population. This is easily understood using the following example. Consider the average return of all stocks listed in the S&P ...