Recall the expected value of a real-valued random variable is the mean of the variable, and is a measure of the center of the distribution. Recall also that by taking the expected value of various tra...Recall the expected value of a real-valued random variable is the mean of the variable, and is a measure of the center of the distribution. Recall also that by taking the expected value of various transformations of the variable, we can measure other interesting characteristics of the distribution. In this section, we will study expected values that measure the spread of the distribution about the mean.
The coupling of measures of centrality and dispersion tells us a lot about the distribution of our data. We can set lower bounds on the percentage of observations that fall in certain ranges regardles...The coupling of measures of centrality and dispersion tells us a lot about the distribution of our data. We can set lower bounds on the percentage of observations that fall in certain ranges regardless of the distribution; this result is called Chebyshev's Inequality. If we restrict our interest to a class of distributions called normal distributions, we can specify precisely the percentage of observations that fall in certain ranges; this result is called the Empirical Rule.
