Use a study, news article, or textbook example that utilizes descriptive statistics in a business setting. You can do a search on the internet to find studies or news articles from well

Bloomberg Businessweek

1.1 Applications in Business and Economics

Accounting firms use statistical sampling procedures when conducting audits for their clients. After reviewing the accuracy of the sampl ed accounts, the auditors draw a conclusion as to whether the accounts receivable amount shown on the client's balance sheet is acceptable .

Financial analysts use statistical information to guide their investment recommendations. For example, comparing the dividend yield for Microsoft to the average dividend yield for S&P 500 companies can help the analyst determine whether to recommend buying, selling, or hold ing Microsoft stock.

Marketing Electronic scanners at retail checkout counters collect data for a variety of marketing research applications. Manufacturers spend hundreds of thousands of dollars per product category to obtain this type of scanner data. Brand managers can review the scanner statisti cs and the promotional activity statistics to gain a better understanding of the relationship between promotional activities and sales.

Production Today’s emphasis on quality makes quality control an important application of statistics in production. A variety of statisti cal quality control charts are used to monitor the output of a production process. Properly interpreted, an x -bar chart can help determine when adjustments are necessary to correct a production process.

Economics Economists frequently provide forecasts about the future of the economy or some aspect of it. For instance, in forecasting in flation rates, economists use statistical information on such indicators as the Producer Price Index, the unemployment rate, and manufacturing capacity utilization.

Information Systems Information systems administrators are responsible for the day-to-day operation of an organization’s computer networks. Statistics such as the mean number of users on the system, the proportion of time any component of the system is down, and the proportion of bandwidth ut ilized at various times of the day, are examples of statistical information that help the system administrator better understand and manage the computer network. Such examples provide an overview of the breadth of statistical applications. To supplement these examples, practitioners in the fields of business and economics provided chapter-opening Statistics in Practice articles that introduce the material covered in each chapter.

1.2 Data

Data are the facts and figures collected, analyzed, and summarized for presentation and interpretation. All the data collecte d in a particular study are referred to as the data set for the study. Table 1.1

Elements, Variables, and Observations Elements are the entities on which data are collected. A variable is a characteristic of interest for the elements. Measurements collected on each variable for every element in a study provide the data. The set of measurements obtained for a particular e lement is called an observation.

Scale of Measurement Data collection requires one of the following scales of measurement: nominal, ordinal, interval, or ratio.

nominal scale The scale of measurement for a variable when the data are labels or names used to identify an attribute of an element. Nomina l data may be nonnumeric or numeric.

The scale of measurement for a variable is considered an ordinal scale if the data exhibit the properties of nominal data and in addition, the order or rank of the data is meaningful.

The scale of measurement for a variable is an interval scale if the data have all the properties of ordinal data and the inte rval between values is expressed in terms of a fixed unit of measure. Interval data are always numeric.

Week 1 – Ch1 Sunday, June 4, 2023 4:57 PM

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The scale of measurement for a variable is a ratio scale if the data have all the properties of interval data and the ratio o f two values is meaningful. Such as, distance, height, weight, and time use the ratio scale of measurement.

Categorical and Quantitative Data Data can be classified as either categorical or quantitative. categorical data. Categorical data use either the nominal or ordinal scale of measurement. Data that use numeric values to in dicate how much or how many are referred to as quantitative data. Quantitative data are obtained using either the interval or ratio scale of measure ment.

The statistical method appropriate for summarizing data depends upon whether the data are categorical or quantitative.

A categorical variable is a variable with categorical data, and a quantitative variable is a variable with quantitative data.

Cross-Sectional and Time Series Data

Cross-sectional data are data collected at the same or approximately the same point in time. Time series data are data collected over several time periods.

Notes and Comments An observation is the set of measurements obtained for each element in a data set. Hence, the number of observations is alway s the same as the number of elements. The number of measurements obtained for each element equals the number of variables. Hence, the total num ber of data items can be determined by multiplying the number of observations by the number of variables.

Quantitative data may be discrete or continuous. Quantitative data that measure how many (e.g., number of calls received in 5 minutes) are discrete. Quantitative data that measure how much (e.g., weight or time) are continuous because no separation occurs between the possib le data values.

1.3 Data Sources

Data can be obtained from existing sources, by conducting an observational study, or by conducting an experiment.

Companies access these external data sources through leasing arrangements or by purchase. Dun & Bradstreet, Bloomberg, and Dow Jones & Company are three firms that provide extensive business database services to clients.

Government agencies are another important source of existing data. For instance, the website DATA.GOV was launched by the U.S. government in 2009 to make it easier for the public to access data collected by the U.S. federal government.

Observational Study what is happening in a particular situation, record data on one or more variables of interest, and conduct a statistical analysis of the resulting data.

Experiment The largest experimental statistical study ever conducted is believed to be the 1954 Public Health Service experiment for the Salk polio vaccine. Nearly 2 million children in grades 1, 2, and 3 were selected from throughout the United States.

The key difference between an observational study and an experiment is that an experiment is conducted under controlled conditions.

Time and Cost Issues

Data Acquisition Errors erroneous data can be worse than not using any data at all.

Errors often occur during data acquisition.

1.4Descriptive Statistics

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1.4Descriptive Statistics Most of the statistical information in the media, company reports, and other publications consists of data that are summarize d and presented in a form that is easy for the reader to understand. Such summaries of data, which may be tabular, graphical, or numerical, are referre d to as descriptive statistics.

In addition to tabular and graphical displays, numerical descriptive statistics are used to summarize data. The most common n umerical measure is the average, or mean.

1.5Statistical Inference

Many situations require information about a large group of elements (individuals, companies, voters, households, products, cu stomers, and so on)

The larger group of elements in a particular study is called the population, and the smaller group is called the sample.

Population A population is the set of all elements of interest in a particular study.

Sample A sample is a subset of the population.

The process of conducting a survey to collect data for the entire population is called a census. The process of conducting a survey to collect data for a sample is called a sample survey. As one of its major contributions, statistics uses data from a sample to make estimates and test hypotheses about the chara cteristics of a population through a process referred to as statistical inference.

1.6Statistical Analysis Using Microsoft Excel

Our focus is on showing the appropriate statistical procedures for collecting, analyzing, presenting, and interpreting data.

Data Sets and Excel Worksheets To hide rows 15 through 54 of the

Using Excel for Statistical Analysis

Enter/Access Data: Select cell locations for the data and enter the data along with appropriate labels; or open an existing Excel file such as one of the files that accompany the text.

Enter Functions and Formulas: Select cell locations, enter Excel functions and formulas, and provide descriptive labels to identify the results.

Apply Tools: Use Excel’s tools for data analysis and presentation.

Editing Options: Edit the results to better identify the output or to create a different type of presentation.

the formula =MEDIAN(A2:A201)

1.7Analytics

We adopt the definition of analytics developed by the Institute for Operations Research and the Management Sciences (INFORMS) .

Analytics is the scientific process of transforming data into insights for making better decisions. Used for date -driven or fact-based decision making.

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Descriptive analytics encompasses the set of analytical techniques that describe what has happened in the past. Examples of these types of techniques are data queries, reports, descriptive statistics, data visualization, data dash boards, and basic what-if spreadsheet models.

Predictive analytics consists of analytical techniques that use models constructed from past data to predict the future or to assess the impact of one variable on another. For example, past data on sales of a product may be used to construct a mathematical model that predicts future sales. Such a model can account for factors such as the growth

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construct a mathematical model that predicts future sales. Such a model can account for factors such as the growth trajectory and seasonality of the product’s sales based on past growth and seasonal patterns.

Prescriptive analytics differs greatly from descriptive or predictive analytics. What distinguishes prescriptive analytics is that prescriptive models yield a best course of action to take. That is, the output of a prescriptive model is a best decision. Hence, prescriptive analytics is the set of analytical techniques that yield a course of action. Optimization models, which generate solutions that maximize or minimize some objective subject to a set of constraints, fall into the category of prescriptive models. The airline industry’s use of revenue management is an example of a prescriptive model. The airline industry uses past purchasing data as inputs into a model that recommends the pricing strategy across all flights that will maximize revenue for the company.

How does the study of statistics relate to analytics? Most of the techniques in descriptive and predictive analytics come from probability and statistics. These include descriptive statistics, data visualization, probability and probability distributions, sampling, and predictive modeling, including regression analysis and time series forecasting. Each of these techniques is discussed in this text. The increased use of analytics for data-driven decision making makes it more important than ever for analysts and managers to understand statistics and data analysis. Companies are increasingly seeking data savvy managers who know how to use descriptive and predictive models to make data – driven decisions.

At the beginning of this section, we mentioned the increased availability of data as one of the drivers of the interest in analytics. In the next section we discuss this explosion in available data and how it relates to the study of statistics.

1.8Big Data and Data Mining

Larger and more complex data sets are now often referred to as big data.

Volume refers to the amount of available data (the typical unit of measure for data is now a terabyte,

which is bytes); velocity refers to the speed at which data is collected and

processed; variety refers to the different data types; and veracity refers to the reliability of the data generated.

data warehousing is used to refer to the process of capturing, storing, and maintaining the data.

data mining deals with methods for developing useful decision-making information from large databases.

Data mining is a technology that relies heavily on statistical methodology such as multiple regression, logistic regression, and correlation.

1.9Ethical Guidelines for Statistical Practice

The American Statistical Association, the nation’s leading professional organization for statistics and statisticians, develo ped the report “Ethical Guidelines for Statistical Practice”

Summary Statistics is the art and science of collecting, analyzing, presenting, and interpreting data. Nearly every college student majoring in business or economics is required to take a course in statistics. We began the chapter by describing typical statistical applications for business and economics.

Data consist of the facts and figures that are collected and analyzed. The four scales of measurement used to obtain data on a particular variable are nominal, ordinal, interval, and ratio. The scale of measurement for a variable is nominal when the data are labels or names used to identify an attribute of an element. The scale is ordinal if the data demonstrate the properties of nominal data and the order or rank of the data is meaningful. The scale is interval if the data demonstrate the properties of ordinal data and the interval between values is expressed in terms of a fixed unit of measure. Finally, the scale of measurement is ratio if the data show all the properties of interval data and the ratio of two values is meaningful.

For purposes of statistical analysis, data can be classified as categorical or quantitative. Categorical data use labels or names to identify an attribute of each element. Categorical data use either the nominal or ordinal scale of measurement

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names to identify an attribute of each element. Categorical data use either the nominal or ordinal scale of measurement and may be nonnumeric or numeric. Quantitative data are numeric values that indicate how much or how many. Quantitative data use either the interval or ratio scale of measurement. Ordinary arithmetic operations are meaningful only if the data are quantitative. Therefore, statistical computations used for quantitative data are not always appropriate for categorical data.

In Sections 1.4 and 1.5 we introduced the topics of descriptive statistics and statistical inference. Descriptive statistics are the tabular, graphical, and numerical methods used to summarize data. The process of statistical inference uses data obtained from a sample to make estimates or test hypotheses about the characteristics of a population. The last four sections of the chapter provide information on the role of computers in statistical analysis, an introduction to the relatively new fields of analytics, data mining, and big data, and a summary of ethical guidelines for statistical practice.

Glossary Analytics▪

Big Data▪

Categorical data▪

Categorical variable▪

Census▪

Cross-sectional data▪

Data▪

Data mining▪

Data set▪

Descriptive Analytics▪

Descriptive statistics▪

Elements▪

Interval scale▪

Nominal scale▪

Observation▪

Ordinal scale▪

Population▪

Predictive Analytics▪

Prescriptive Analytics▪

Quantitative data▪

Quantitative variable▪

Ratio scale▪

Sample▪

Sample survey▪

Statistical inference▪

Statistics▪

Time series data▪

Variable▪

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