Reading 8 Statistical Concepts and Market Returns Introduction
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Statistical methods provide a powerful set of tools for analyzing data and drawing conclusions from them. Whether we are analyzing asset returns, earnings growth rates, commodity prices, or any other financial data, statistical tools help us quantify and communicate the data’s important features. This reading presents the basics of describing and analyzing data, the branch of statistics known as descriptive statistics. The reading supplies a set of useful concepts and tools, illustrated in a variety of investment contexts. One theme of our presentation, reflected in the reading’s title, is the demonstration of the statistical methods that allow us to summarize return distributions.1 We explore four properties of return distributions:
where the returns are centered (central tendency);
how far returns are dispersed from their center (dispersion);
whether the distribution of returns is symmetrically shaped or lopsided (skewness); and
whether extreme outcomes are likely (kurtosis).
These same concepts are generally applicable to the distributions of other types of data, too.
The reading is organized as follows. After defining some basic concepts in Section 2, in Sections 3 and 4 we discuss the presentation of data: Section 3 describes the organization of data in a table format, and Section 4 describes the graphic presentation of data. We then turn to the quantitative description of how data are distributed: Section 5 focuses on measures that quantify where data are centered, or measures of central tendency. Section 6 presents other measures that describe the location of data. Section 7 presents measures that quantify the degree to which data are dispersed. Sections 8 and 9 describe additional measures that provide a more accurate picture of data. Section 10 provides investment applications of concepts introduced in Section 5.