Some General Thoughts about Statistics

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The first and most important concept to consider in a study of statistics is that it is, among other things, a way of working with sets of numbers. That is, we use statistics to gain information about and understanding of collections of numbers. When we use the word statistics in this way, we are speaking about a set of concepts, procedures, and techniques that enable us to extract meaningful information from groups of numbers. It is, in this sense, an area of mathematics. We may also use the term statistics to refer to a collection of numbers. In that sense we may say, "I need some statistics about our county residents in order to complete this proposal" There are other meanings of the word as well. We may speak about a statistic, as in, "He had become nothing more than a statistic to the insurance company." When we use the word in this way we are treating a person or object as if it were nothing more than a number. Another way a statistic can be a single number is when we calculate something like an average score. In this case, the average score is said to be a statistic.

Another important concept to understand when studying statistics is that this is an area of mathematics that is entirely practical. That is, it is an area of applied mathematics rather than an area of theoretical, or pure, mathematics. Because of this, many mathematicians are reluctant to even consider statistics to be a legitimate area of mathematical study. In some colleges, courses in statistics are handled completely outside the department of mathematics. Statistics may be a course taught in a business department, a sociology department, a psychology department, or even a science department. Because of its wide application to real-world problems, statistics has become a vital part of our scientific, technological, commercial, and political worlds. One cannot truly understand science without an understanding of statistics. The same can be said about social science. Certainly political events are saturated with statistics, as one can see from even a cursory examination of any daily newspaper. Advertisers constantly make clever and often deceptive use of statistics.

Through manipulation and distortion of statistics, many people use the power of mathematics to mislead and control those who have an unsophisticated understanding of statistics. Many people who lack a deep understanding of statistics become disillusioned when it seems as if everyone uses numbers to prove opposing sides of controversial issues. Because of these issues, much of our examination of statistics focuses on how people use and misuse statistical information. We present some tricks and techniques for distortion, not because we believe our readers will want to use them, but because we believe that teachers must equip children to discern and unmask these techniques on a daily basis if they are to become intelligent, participatory citizens in a democratic society.