------------------------------------------------- Ch 1 Introduction 1.1 Why Learn Statistics? * Statistics is the branch of mathematics that transforms numbers into useful information for decision makers. Statistics lets you know about the risks associated with making a business decision and allows you to understand and reduce the variation in the decision-making process. * Statistics provides you with methods for making better sense of the numbers used every day to describe or analyze the world we live in. * Statistical methods help you understand the information contained in “the numbers” and determine whether differences in “the numbers are meaningful or just due to chance. * Why learn statistics? First and foremost, statistics helps you make better sense of the world. Second, statistics helps you make better business decisions. 1.2 Statistics in Business * In the business world, statistics has these important specific uses: 1. To summarize business data 2. To draw conclusions from those data 3. To make reliable forecasts about business activities 4. To improve business processes * The statistical methods you use for these tasks come from one of the two branches of statistics: descriptive statistics and inferential statistics. * Descriptive statistics are the methods that help collect, summarize, present, and analyze a set of data. * Inferential statistics are the methods that use the data collected from a small group to draw conclusions about a larger group. * Many of the tables and charts found in a typical presentation are the products of descriptive methods, as are statistics such as the mean or median of a group. When you use statistical methods to help choose which investment from a set of investments might lead to a higher return or which marketing strategy might lead to increased sales, you are using inferential methods. * There are four important uses of statistics in business: 1. Using descriptive methods to visualize and summarize your data. 2. Using inferential methods to reach conclusions about a large group based on data collected from a small group. 3. Making reliable forecasts involves developing statistical models for prediction. These models use inferential methods to increase the accuracy of predictions made about future activities. 4. Improving business processes involves using managerial approaches such as Six Sigma that focus on quality improvement. * To use descriptive and inferential methods correctly, you must also learn the conditions and assumptions required for using those methods. And because many of the statistical methods used in business must be computerized in order to be of practical benefit, you also need to know how computers can help you apply statistics in the business world. 1.3 Basic Vocabulary of Statistics * Seven terms – variable, data, operational definition, population, sample, parameter, and statistic (singular) – identify the fundamental concepts of statistics. * Variables are characteristics of items or individuals and are what you analyze when you use a statistical method. When used in everyday speech, variable suggests that something changes or varies, and you would expect sales, expenses, and net profit to have different values from year to year. These different values are the data associated with a variable or, more simply, the “data to be analyzed.” * A variable is a characteristics of an item or individual. * Data are the different values associated with a variable. * Variables can differ for reasons other than time. Variable values are meaningless unless their corresponding variables have operational definitions. These definitions are universally accepted meanings that are clear to all associated with an analysis. Even individual values for variables sometimes need definition. * The subject of statistics creates useful information from either populations or samples. * A population consists of all the items or individuals about which you want to draw a conclusion. * A sample is the portion of a population selected for analysis. * Parameter and statistic complete the basic vocabulary of statistics. * A parameter is a measure that describes a characteristic of a population. * A statistic is a measure that describes a characteristic of a sample. ------------------------------------------------- Ch 2 Organizing and Visualizing Data Xu, Jian * DCOVA: Define, Collect, Organize, Visualize, and Analyze: 1. Define the variables that you want to study in order to solve a business problem or meet a business objective. 2. Collect the data from appropriate sources. 3. Organize the data collected by developing tables. 4. Visualize the data by developing charts. 5. Analyze the data by examining the appropriate tables and charts to reach conclusions. 2.1 Types of Variables * Defining a variable includes establishing its type. You classify variables as either being categorical or numerical and further classify numerical variables as having either discrete or continuous variables. * Categorical variables (also known as qualitative variables) have values that can only be placed into categories such as yes and no. * Numerical variables (also known as quantitative variables) have values that represent quantities. Numerical variables are further subdivided as discrete or continuous variables. * Discrete variables have numerical values that arrive from a counting process. The response is one of a finite number of integers. * Continuous variables produce numerical responses that arise from a measuring process. The response takes on any value within a continuum, or interval, depending on the precision of the measuring instrument. * Theoretically, with sufficient precision of measurement, no two continuous values are identical. As a practical matter, however, most measuring devices are not precise enough to detect small differences, and tied values for a continuous variable (two or more items or individuals with the same value) are sometimes present in experimental or survey data. * Levels of Measurement and Measurement Scales * Using levels of measurement is another way of classifying data. There are four widely recognized levels of measurement: nominal, ordinal, interval, and ratio scales. Nominal and Ordinal Scales * Data from a categorical variable are measured on a nominal scale or on an ordinal scale. * A nominal scale classifies data into distinct categories in which no ranking is implied. * Nominal scaling is the weakest form of measurement because you cannot specify any ranking across the various categories. * An ordinal scale classifies data into distinct categories in which ranking is implied. * Ordinal scaling is a stronger form of measurement than nominal scaling because an observed value classified into one category possess more of a property than does an observed value classified into another category. However, ordinal scaling is still a relatively weak form of measurement because the scale does not account for the amount of the differences between the categories. The ordering implies only which category is “greater,” “better,” or “more preferred” – not by how much. Interval and Ratio Scales * Data from a numerical variable are measured on an interval or a ratio scale. * An interval scale is an ordered scale in which the difference between measurements is a meaningful quantity but does not involve a true zero point. * A ratio scale is an ordered scale in which the difference between the measurements involves a true zero point, as in height, weight, age, or salary measurements. * Data measured on an interval scale or on a ratio scale constitute the highest levels of measurement. They are stronger forms of measurement than an ordinal scale because you can determine not only which observed value is the largest but also by how much. 2.2 Data Collection * In many situations, you need to collect the data for the variables you have defined. * Data collection almost always involves collecting data from a sample because collecting data from every item or individual in a population is typically too difficult or too time-consuming. * When you collect data, you use either a primary data source or a secondary data source. When you are collecting your own data for your own analysis, the data source is a primary one. When the data collector and analyst are not the same, the source is secondary. *