If two countries have the same average life expectancy over two decades, does that fact imply that the life expectancies are the same for those countries? What information would you like to know in addition to the overall life expectancy after two decades? If two professional baseball players from two different decades have the same batting average, does that imply they both performed equally well compared to their peers? How can college admissions officers compare the qualifications of applicants who have taken different entrance exams (for example, the ACT vs. the SAT)? The answers to these questions lie in studying the spread—or consistency—of distributions. In this topic, you will even discover how the spread of a distribution relates to the midnight ride of Paul Revere!
In the previous topic, you explored the mean and median, important numerical measures of the center of a distribution. In this topic, you will build on your knowledge of measures of center by investigating similar numerical measures of a distribution's spread, or variability, namely the interquartile range and the standard deviation. You will examine these measures' properties and investigate some common misconceptions about variability. Studying these measures will also lead you to an important result (the empirical rule) and an important technique (standardization, or computing z-scores)—two concepts that will appear throughout this course.