CHAPTER 1: INTRODUCTION

WHAT IS STATISTICS? Definition Statistics is a group of methods used to collect, analyze, present, and interpret data and to make decisions.

TYPES OF STATISTICS Definition Descriptive Statistics consists of methods for organizing, displaying, and describing data by using tables, graphs, and summary measures.

TYPES OF STATISTICS Definition Inferential Statistics consists of methods that use sample results to help make decisions or predictions about a population.

POPULATION VERSUS SAMPLE Definition A population consists of all elements – individuals, items, or objects – whose characteristics are being studied. The population that is being studied is also called the target population.

POPULATION VERSUS SAMPLE cont. Definition A portion of the population selected for study is referred to as a sample.

Figure 1.1 Population and sample.

POPULATION VERSUS SAMPLE cont. Definition A survey that includes every member of the population is called a census. The technique of collecting information from a portion of the population is called a sample survey.

POPULATION VERSUS SAMPLE cont. Definition A sample that represents the characteristics of the population as closely as possible is called a representative sample.

POPULATION VERSUS SAMPLE cont. Definition A sample drawn in such a way that each element of the population has a chance of being selected is called a random sample. If the chance of being selected is the same for each element of the population, it is called a simple random sample.

An observation or measurement BASIC TERMS Table 1.1 2001 Sales of Seven U.S. Companies Company 2001 Sales (millions of dollars) Wal-Mart Stores IBM General Motors Dell Computer Procter & Gamble JC Penney Home Depot 217,799 85,866 177,260 31,168 39,262 32,004 53,553 Variable An observation or measurement An element or a member

BASIC TERMS cont. Definition An element or member of a sample or population is a specific subject or object (for example, a person, firm, item, state, or country) about which the information is collected.

BASIC TERMS cont. Definition A variable is a characteristic under study that assumes different values for different elements. In contrast to a variable, the value of a constant is fixed.

BASIC TERMS cont. Definition The value of a variable for an element is called an observation or measurement.

BASIC TERMS cont. Definition A data set is a collection of observations on one or more variables.

TYPES OF VARIABLES Quantitative Variables Discrete Variables Continuous Variables Qualitative or Categorical Variables

Quantitative Variables Definition A variable that can be measured numerically is called a quantitative variable. The data collected on a quantitative variable are called quantitative data.

Quantitative Variables cont. Definition A variable whose values are countable is called a discrete variable. In other words, a discrete variable can assume only certain values with no intermediate values.

Quantitative Variables cont. Definition A variable that can assume any numerical value over a certain interval or intervals is called a continuous variable.

Qualitative or Categorical Variables Definition A variable that cannot assume a numerical value but can be classified into two or more nonnumeric categories is called a qualitative or categorical variable. The data collected on such a variable are called qualitative data.

Figure 1.2 Types of variables.

CROSS-SECTION VERSUS TIME-SERIES DATA Cross-Section Data Time-Series Data

Cross-Section Data Definition Data collected on different elements at the same point in time or for the same period of time are called cross-section data.

Table 1.2 2002 Net Worth of Six Persons Name 2002 Net Worth (billions of dollars) Bill Gates Warren Buffett Helen Walton George Lucas Ted Turner Ralph Lauren 43.0 36.0 18.8 3.0 2.2 2.0

Time-Series Data Definition Data collected on the same element for the same variable at different points in time or for different periods of time are called time-series data.

Price of a 30-Second TV Commercial (million dollars) Table 1.3 Price of a 30-Second TV Commercial During Super Bowl Telecast Year Super Bowl Price of a 30-Second TV Commercial (million dollars) 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 XXVII XXVIII XXIX XXX XXXI XXXII XXXIII XXXIV XXXV XXXVI XXXVII .85 .90 1.00 1.10 1.20 1.30 1.60 2.10 2.05 1.90 2.20

SOURCES OF DATA Data may be obtained from Internal sources External sources Surveys and experiments

SUMMATION NOTATION Example 1-1 Annual salaries (in thousands of dollars) of four workers are 75, 42, 125, and 61. Find ∑x (∑x)² ∑x²

Solution 1-1 ∑x = x1 + x2 + x3 + x4 = 75 + 42 + 125 + 61 = 303 = $303,000 (∑x)² = (303)² = 91,809 ∑x² = (75)² + (42)² + (125)² + (61)² = 5625 + 1764 + 15,625 + 3721 = 26,735

Example 1-2 The following table lists four pairs of m and f values: Compute the following: Σm Σf² Σmf Σm²f m 12 15 20 30 f 5 9 10 16

Solution 2-1 Table 1.4 m f f² mf m²f 12 15 20 30 5 9 10 16 5 x 5 = 25 12 x 12 x 5 = 720 15 x 15 x 9 = 2025 20 x 20 x 10 = 4000 30 x 30 x 16 = 14,400 ∑m = 77 ∑f = 40 ∑f² = 462 ∑mf = 875 ∑m²f = 21,145