Fundamentals of Statistics

Every day, you encounter numerical information that describes or analyzes some aspect of the world you live in. For example, here are some news items that appeared in the pages of The New York Times during a one-month period:

• Between 1969 and 2001, the rate of forearm fractures rose 52% for girls and 32% for boys, with the largest increases among children in early puberty, according to a recent Mayo Clinic study.

• Across the New York metropolitan area, the median sales price of a single-family home has risen by 75% since 1998, an increase of more than $140,000.

• A study that explored the relationship between the price of a book and the number of copies of a book sold found that raising prices by 1% reduced sales by 4% at BN.com, but reduced sales by only 0.5% at Amazon.com.

Such stories as these would not be possible to understand without statistics, the branch of mathematics that consists of methods of processing and analyzing data to better support rational decision-making processes. Using statistics to better understand the world means more than just producing a new set of numerical information—you must interpret the results by reflecting on the significance and the importance of the results to the decision-making process you face. Interpretation also means knowing when to ignore results, either because they are misleading, are produced by incorrect methods, or just restate the obvious, as this news story “reported” by the comedian David Letterman illustrates:

USA Today has come out with a new survey. Apparently, 3 out of every 4 people make up 75% of the population.

As newer technologies allow people to process and analyze ever-increasing amounts of data, statistics plays an increasingly important part of many decision-making processes today. Reading this chapter will help you understand the fundamentals of statistics and introduce you to concepts that are used throughout this book.