Basic Skills and Principles: Statistics and Graphing

Statistics
An Introduction

Statistics - they're all around us, and we're exposed to them every day. They allow us to summarize large volumes of mathematical information, and so are found wherever there's data to be presented. Let's say you're watching your favorite college football team, and the game has come down to a last second thirty-five yard field goal attempt for the win. When describing the kicker's past performance in this range, the play-by-play announcer doesn't list all of the kicker's attempts one by one and their outcome, he simply states the percentage of kicks made in this yard range. If the kicker's success rate from 30-40 yards has been 90% this season, then you're feeling pretty confident of victory. If it's 40%, you're gripping the chair a little tighter when the ball is snapped.

The most recognizable use of statistics for the typical college student is when exam grades are posted. You want to know two things: your score and the class average. The class average matters because it is an easy way for you to compare your performance with the "average" student in the class, and to get an idea for the potential for the "curving" of exam scores.

If you're a sports fan, statistics can be important when comparing players' performance, determining success or failure in fantasy sports leagues, and in the all-too-frequent debates on the greatest players of all time. They allow you to quickly summarize an entire player's career or performance into a few numbers, and to make comparisons between players for the same statistic. Statistics also play a prominent role in politics, where supporters or detractors of legislation often use statistics to back their position and discredit their opponents' point of view. When politicians are proposing tax cuts, opponents of the cut will state the the vast majority of the benefit goes to the top 1% of taxpayers, while proponents will state that the average taxpayer stands to have their tax burden reduced by a sizable amount. In many of these cases, both sides are using the same data source and are technically telling the truth, but the impression one gets from the two points of view is radically different. Advertising works in much the same way, where commercials will present statistics from industry ratings (automobile ratings, consumer research studies) that show their products favorably and their competitor's products unfavorably. Curiously enough, their competitor will run a commercial giving the exact opposite impression while citing the same source. The National Public Radio piece below describes some examples of how individuals can use statistics, sometimes in a misleading manner, to bolster their arguments.

The gathering and analysis of data forms the backbone of science, and so statistics obviously play an important role in this discipline. Statistics are used to describe numerous parameters (temperature, growth rates, age, etc.) and to make comparisons between experimental groups. In this week's exercise, you will be given an introduction to statistics, with emphasis on the statistical measures you will be using throughout the semester to analyze and present data. We will begin by examining descriptive statistics, which are used to summarize groups of data. We will then cover data presentation, in which the proper methods for displaying data in tables and figures will be described. You will frequently be using the skills you learn here throughout the semester, so you are strongly encouraged to review the material in this exercise diligently.