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Fundamentals of Statistics

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You can make better sense of the numbers you encounter if you learn to understand statistics. In this chapter, you begin by learning five basic words--population, sample, variable, parameter, and statistic (singular)--that identify the fundamental concepts of statistics.
This chapter is from the book
  • 1.1 The First Three Words of Statistics
  • 1.2 The Fourth and Fifth Words
  • 1.3 The Branches of Statistics
  • 1.4 Sources of Data
  • 1.5 Sampling Concepts
  • 1.6 Sample Selection Methods One-Minute Summary Test Yourself

Every day, the media uses numbers to describe or analyze our world:

  • “6 New Facts About Facebook” (A. Smith,www.pewresearch.org/author/asmith, 3 February 2014). A survey reported that women were more likely than men to cite seeing photos or videos, sharing with many people at once, seeing entertaining or funny posts, learning about ways to help others, and receiving support from people in their network as reasons to use Facebook.
  • “First Two Years of College Wasted?” (M. Marklein, USA Toda, 18 January 2011, p. 3A). A survey of more than 3,000 full-time, traditional-age students found that the students spent 51% of their time on socializing, recreation, and other activities; 9% of their time attending class and labs; and 7% of their time studying.
  • “Follow the Tweets” (H. Rui, A. Whinston, and E. Winkler, The Wall Street Journal, 30 November 2009, p. R4). In this study, the authors found that the number of times a specific product was mentioned in comments in the Twitter social messaging service could be used to make accurate predictions of sales trends for that product.

You can make better sense of the numbers you encounter if you learn to understand statistics. Statistics, a branch of mathematics, uses procedures that allow you to correctly analyze the numbers. These procedures, or statistical methods, transform numbers into useful information that you can use when making decisions about the numbers. Statistical methods can also tell you the known risks associated with making a decision as well as help you make more consistent judgments about the numbers.

Learning statistics requires you to reflect on the significance and the importance of the results to the decision-making process you face. This statistical interpretation means knowing when to ignore results because they are misleading, are produced by incorrect methods, or just restate the obvious, as in “100% of the authors of this book are named ‘David.’”

In this chapter, you begin by learning five basic words—population, sample, variable, parameter, and statistic (singular)—that identify the fundamental concepts of statistics. These five words, and the other concepts introduced in this chapter, help you explore and explain the statistical methods discussed in later chapters.

1.1 The First Three Words of Statistics

You’ve already learned that statistics is about analyzing things. Although numbers was the word used to represent things in the opening of this chapter, the first three words of statistics, population, sample, and variable, help you to better identify what you analyze with statistics.

Population

CONCEPT All the members of a group about which you want to reach a conclusion.

EXAMPLES All U.S. citizens who are currently registered to vote, all patients treated at a particular hospital last year, the entire set of individuals who accessed a website on a particular day.

Sample

CONCEPT The part of the population selected for analysis.

EXAMPLES The registered voters selected to participate in a recent survey concerning their intention to vote in the next election, the patients selected to fill out a patient satisfaction questionnaire, 100 boxes of cereal selected from a factory’s production line, 500 individuals who accessed a website on a particular day.

Variable

CONCEPT A characteristic of an item or an individual that will be analyzed using statistics.

EXAMPLES Gender, the party affiliation of a registered voter, the household income of the citizens who live in a specific geographical area, the publishing category (hardcover, trade paperback, mass-market paperback, textbook) of a book, the number of cell phones in a household.

INTERPRETATION All the variables taken together form the data of an analysis. Although people often say that they are analyzing their data, they are, more precisely, analyzing their variables.

You should distinguish between a variable, such as gender, and its value for an individual, such as male. An observation is all the values for an individual item in the sample. For example, a survey might contain two variables, gender and age. The first observation might be male, 40. The second observation might be female, 45. The third observation might be female, 55. By convention, when you organize data in tabular form, you place the values for a variable to be analyzed in a column. Therefore, some people refer to a variable as a column of data. Likewise, some people call an observation a row of data.

Categorical Variables

Numerical Variables

Concept

The values of these variables are selected from an established list of categories.

The values of these variables involve a counted or measured value.

Subtypes

None

Discrete values are counts of things.

Continuous values are measures and any value can theoretically occur, limited only by the precision of the measuring process.

Examples

Gender, a variable that has the categories “male” and “female.” variable.

Academic major, a variable that might have the categories “English,” “Math,” “Science,” and “History,” among others.

The number of people living in a household, a discrete numerical

The time it takes for someone to commute to work, a continuous variable.

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