University:
California State University, Northridge
Course:
MATH 140 | Introductory Statistics
Academic year:

2024
Views:

202

Pages:

39
Author:

Kody Downs

Chapter 1 - Data and Statistics • • • • • • • • • • Statistics Applications in Business and Economics Data Data Sources Descriptive Statistics Statistical Inference Analytics Big Data and Data Mining Computers and Statistical Analysis Ethical Guidelines for Statistical Practice 2 What is Statistics? • The term statistics can refer to numerical facts such as averages, medians, percentages, and maximums that help us understand a variety of business and economic situations. • Statistics can also refer to the art and science of collecting, analyzing, presenting, and interpreting data. 3 Applications in Business and Economics Accounting • Public accounting firms use statistical sampling procedures when conducting audits for their clients. Economics • Economists use statistical information in making forecasts about the future of the economy or some aspect of it. Finance • Financial advisors use price-earnings ratios and dividend yields to guide their investment advice. 4 Applications in Business and Economics Marketing • Electronic point-of-sale scanners at retail checkout counters are used to collect data for a variety of marketing research applications. Production • A variety of statistical quality control charts are used to monitor the output of a production process. Information Systems • A variety of statistical information helps administrators assess the performance of computer networks. 5 Data and Data Sets • Data are the facts and figures collected, analyzed, and summarized for presentation and interpretation. • All the data collected in a particular study are referred to as the data set for the study. 6 Elements, Variables, and Observations • Elements are the entities on which data are collected. • A variable is a characteristic of interest for the elements. • The set of measurements obtained for a particular element is called an observation. • A data set with n elements contains n observations. • The total number of data values in a complete data set is the number of elements multiplied by the number of variables. 7 Data, Data Sets, Elements, Variables, and Observations Variables Element Names Company Stock Exchange Annual Sales ($M) Earnings per share ($) Dataram NQ 73.10 0.86 EnergySouth N 74.00 1.67 Keystone N 365.70 0.86 LandCare NQ 111.40 0.33 N 17.60 0.13 Psychemedics Observation Data Set 8 Scales of Measurement • Scales of measurement include • • • • Nominal Ordinal Interval Ratio • The scale determines the amount of information contained in the data. • The scale indicates the data summarization and statistical analyses that are most appropriate. 9 Scales of Measurement Nominal scale • Data are labels or names used to identify an attribute of the element. • A nonnumeric label or numeric code may be used. Example Students of a university are classified by the school in which they are enrolled using a nonnumeric label such as Business, Humanities, Education, and so on. Alternatively, a numeric code could be used for the school variable (e.g. 1 denotes Business, 2 denotes Humanities, 3 denotes Education, and so on). 10 Scales of Measurement Ordinal scale • The data have the properties of nominal data and the order or rank of the data is meaningful. • A nonnumeric label or numeric code may be used. Example Students of a university are classified by their class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior. Alternatively, a numeric code could be used for the class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on). 11 Scales of Measurement Interval scale • The data have the properties of ordinal data, and the interval between observations is expressed in terms of a fixed unit of measure. • Interval data are always numeric. Example Melissa has an SAT score of 1985, while Kevin has an SAT score of 1880. Melissa scored 105 points more than Kevin. 12 Scales of Measurement Ratio scale • Data have all the properties of interval data and the ratio of two values is meaningful. • Ratio data are always numerical. • Zero value is included in the scale. Example: Price of a book at a retail store is $ 200, while the price of the same book sold online is $100. The ratio property shows that retail stores charge twice the online price. 13 Categorical and Quantitative Data • Data can be further classified as being categorical or quantitative. • The statistical analysis that is appropriate depends on whether the data for the variable are categorical or quantitative. • In general, there are more alternatives for statistical analysis when the data are quantitative. 14 Categorical Data • Labels or names are used to identify an attribute of each element • Often referred to as qualitative data • Use either the nominal or ordinal scale of measurement • Can be either numeric or nonnumeric • Appropriate statistical analyses are rather limited 15 Quantitative Data • Quantitative data indicate how many or how much. • Quantitative data are always numeric. • Ordinary arithmetic operations are meaningful for quantitative data. 16 Scales of Measurement Data Categorical Nonnumeric Numeric Nominal Quantitative Ordinal Nominal Numeric Ordinal Interval Ratio 17 Cross-Sectional Data Cross-sectional data are collected at the same or approximately the same point in time. Example Data detailing the number of building permits issued in November 2013 in each of the counties of Ohio. 18 Time Series Data Time series data are collected over several time periods. Example Data detailing the number of building permits issued in Lucas County, Ohio in each of the last 36 months. Graphs of time series data help analysts understand • what happened in the past • identify any trends over time, and • project future levels for the time series 19 Time Series Data Graph of Time Series Data 20 Data Sources Existing Sources • Internal company records – almost any department • Business database services – Dow Jones & Co. • Government agencies - U.S. Department of Labor • Industry associations – Travel Industry Association of America • Special-interest organizations – Graduate Management Admission Council (GMAT) • Internet – more and more firms 21 Data Sources Data Available From Internal Company Records Record Some of the Data Available Employee records Name, address, social security number Production records Part number, quantity produced, direct labor cost, material cost Inventory records Part number, quantity in stock, reorder level, economic order quantity Sales records Product number, sales volume, sales volume by region Credit records Customer name, credit limit, accounts receivable balance Customer profile Age, gender, income, household size 22 Data Sources Data Available From Selected Government Agencies Government Agency Web address Some of the Data Available Census Bureau www.census.gov Population data, number of households, household income Federal Reserve Board www.federalreserve.gov Data on money supply, exchange rates, discount rates Office of Mgmt. & Budget www.whitehouse.gov/omb Data on revenue, expenditures, debt of federal government Department of Commerce www.doc.gov Data on business activity, value of shipments, profit by industry Bureau of Labor Statistics Customer spending, unemployment rate, hourly earnings, safety record www.bls.gov 23 Data Sources Statistical Studies – Observational • In observational (nonexperimental) studies no attempt is made to control or influence the variables of interest. • Example - Survey • Studies of smokers and nonsmokers are observational studies because researchers do not determine or control who will smoke and who will not smoke. 24 Data Sources Statistical Studies – Experimental • In experimental studies the variable of interest is first identified. Then one or more other variables are identified and controlled so that data can be obtained about how they influence the variable of interest. • The largest experimental study ever conducted is believed to be the 1954 Public Health Service experiment for the Salk polio vaccine. Nearly two million U.S. children (grades 1- 3) were selected. 25 Data Acquisition Considerations Time Requirement • Searching for information can be time consuming. • Information may no longer be useful by the time it is available. Cost of Acquisition • Organizations often charge for information even when it is not their primary business activity. Data Errors • Using any data that happen to be available or were acquired with little care can lead to misleading information. 26 Descriptive Statistics • Most of the statistical information in newspapers, magazines, company reports, and other publications consists of data that are summarized and presented in a form that is easy to understand. • Such summaries of data, which may be tabular, graphical, or numerical, are referred to as descriptive statistics. Example The manager of Hudson Auto would like to have a better understanding of the cost of parts used in the engine tune-ups performed in her shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar, are listed on the next slide. 27 Example: Hudson Auto Repair Sample of Parts Cost ($) for 50 Tune-ups 91 78 93 57 75 52 99 80 97 62 71 69 72 89 66 75 79 75 72 76 104 74 62 68 97 105 77 65 80 109 85 97 88 68 83 68 71 69 67 74 62 82 98 101 79 105 79 69 62 73 28 Tabular Summary: Frequency and Percent Frequency Parts Cost ($) Frequency Percent Frequency 50-59 2 4% 60-69 13 26% 70-79 16 32% 80-89 7 14% 90-99 7 14% 100-109 5 10% 50 100% TOTAL 29 Graphical Summary: Histogram Example: Hudson Auto Tune-up Parts Cost 18 16 14 Frequency 12 10 8 6 4 2 0 50-59 60-69 70-79 80-89 90-99 Parts Cost ($) 30 Numerical Descriptive Statistics • The most common numerical descriptive statistic is the mean (or average). • The mean demonstrates a measure of the central tendency, or central location of the data for a variable. • Hudson’s mean cost of parts, based on the 50 tune-ups studied is $79 (found by summing up the 50 cost values and then dividing by 50). 31 Statistical Inference Population: The set of all elements of interest in a particular study. Sample: A subset of the population. Statistical inference: The process of using data obtained from a sample to make estimates and test hypotheses about the characteristics of a population. Census: Collecting data for the entire population. Sample survey: Collecting data for a sample. 32 Process of Statistical Inference Example: Hudson Auto Step 1 Step 2 Step 3 Step 4 • Population consists of all tune ups. Average cost of parts is unknown. • A sample of 50 engine tune-ups is examined. • The sample data provides a sample average parts cost of $79 per tune-up. • The sample average is used to estimate the population average. 33 Analytics Analytics is the scientific process of transforming data into insight for making better decisions. Techniques: • Descriptive analytics: This describes what has happened in the past. • Predictive analytics: Use models constructed from past data to predict the future or to assess the impact of one variable on another. • Prescriptive analytics: The set of analytical techniques that yield a best course of action. 34 Big data and Data Mining: Big data: Large and complex data set. Three V’s of Big data: ⇒Volume : Amount of available data ⇒Velocity: Speed at which data is collected and processed ⇒Variety: Different data types 35 Data warehousing Data warehousing is the process of capturing, storing, and maintaining the data. • Organizations obtain large amounts of data on a daily basis by means of magnetic card readers, bar code scanners, point of sale terminals, and touch screen monitors. • Wal-Mart captures data on 20-30 million transactions per day. • Visa processes 6,800 payment transactions per second. 36 Data Mining • Methods for developing useful decision-making information from large databases. • Using a combination of procedures from statistics, mathematics, and computer science, analysts “mine the data” to convert it into useful information. • The most effective data mining systems use automated procedures to discover relationships in the data and predict future outcomes prompted by general and even vague queries by the user. 37 Data Mining Applications • The major applications of data mining have been made by companies with a strong consumer focus such as retail, financial, and communication firms. • Data mining is used to identify related products that customers who have already purchased a specific product are also likely to purchase (and then pop-ups are used to draw attention to those related products). • Data mining is also used to identify customers who should receive special discount offers based on their past purchasing volumes. 38 Data Mining Requirements • Statistical methodology such as multiple regression, logistic regression, and correlation are heavily used. • Also needed are computer science technologies involving artificial intelligence and machine learning. • A significant investment in time and money is required as well. 39 Data Mining Model Reliability • Finding a statistical model that works well for a particular sample of data does not necessarily mean that it can be reliably applied to other data. • With the enormous amount of data available, the data set can be partitioned into a training set (for model development) and a test set (for validating the model). • There is, however, a danger of overfitting the model to the point that misleading associations and conclusions appear to exist. • Careful interpretation of results and extensive testing is important. 40

Chapter 1 - Data and Statistics

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