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Video Library      Welcome to the Video Library for Quantitative Lessons & Software. As we add videos, we'll note the dates they are added. Also, we are presenting related topics in collections, such as Finance Formulas & Concepts. Video Links & Example Problems (Alphabetical list. Scroll to the list below for descriptions of vocabulary and concepts.) Video Links & Example Problems & Descriptions (Descriptive list. Same list plus descriptions of vocabulary and concepts.) If you need help viewing or listening to the videos, or downloading the free RealOne™video player, Click Plug-ins and Video Tips. Each video runs approximately ten minutes. Looking for videos and example problems to help you study for the Math Practice Test? Click Math Concepts.   Video Links & Example Problems Alpha & Beta Errors Video and Example Problem Binomial Distribution Conditional Probability Creating or Critiquing Data Decision Making Process: Who will win the election? Definitions Descriptive Statistics     Updated 03/23/02 Descriptive Statistics Overview Videos and Example Problem    Added 06/05/01 Confidence Intervals Statistics Estimate Parameters    Added 03/23/02 Calculating Cost    Added 03/23/02 Sample Size Formula to Determine Sample Size    Added 03/23/02 Expected Value Exponential Model     Added 03/23/02 This video also appears in the Finance collection of videos. Finance Formulas & Concepts    Added 03/23/02 We encourage you to study the Finance videos in the order presented below. The models provide a foundation for the formulas and equations discussed in the videos that follow. Notations used in the Finance videos: Superscripts: Some disciplines use the superscript (t) to indicate time (number of years, months, and so on); other disciplines use the superscript (n). The videos below use both references; they are interchangeable. Subscripts: A n and an mean two different things. With A n, you should sum (add) the first n terms. For A 3, you would add the first 3 terms in a sequence of terms. With an, you should find the nth term. For a3, you would find the 3rd term in a sequence of terms. Models (formulas, equations): Additive & Multiplicative Arithmetic Sequence, Part I    Added 03/23/02 Arithmetic Sequence, Part II   Added 03/23/02 Geometric Sequence, Part I    Added 03/23/02 Geometric Sequence, Part II   Added 03/23/02 Simple Interest Simple Interest Formula    Added 03/23/02 Compound Interest We are in the process of correcting the lead in video, Power of Compounding; an error appears at approximately 4:40. In the table of numbers presented, for 30 years, the value of the account should be $300,000; for 40 years, the value of the account should be $930,000. The values of the changes should be adjusted accordingly. Power of Compounding, Introduction   Added 03/23/02 Power of Compounding, Interest Rate    Added 03/23/02 Power of Compounding, Graphing    Added 03/23/02 Visualizing Compounding, Part I    Added 03/23/02 Visualizing Compounding, Part II    Added 03/23/02 Continuous Compounding, Part I    Added 03/23/02 Continuous Compounding, Part II    Added 03/23/02 Average Rate of Return    Added 03/23/02 Nominal & Effective Interest Rates    Added 03/23/02 Present Value Present Value    Added 03/23/02 Annuity Formula Annuity Formula    Added 03/23/02 Capital Recovery Factor Part I, Introduction    Added 03/23/02 Part II, Specific Formula    Added 03/23/02 Part III, General Formula    Added 03/23/02 More Models Exponents    Added 03/23/02 Radicals    Added 03/23/02 Graphing Revenue and Cost Graphing with Straight Lines: Interpret Slope, Y Intercept Inferential Statistics: See Descriptive Statistics Added 03/23/02 Kantian Knowledge Linear Relationship for Price and Demand Mathematics: Relationships and Equations Normal Distribution Order of Operations Subscripted Variables Summation Notation Part I    Added 02/27/02 Part II   Added 02/27/02 Percentages Part I Part II Price and Demand, Linear Relationships Probability Using Tree Diagrams Video and Example Problem Probability Using Venn Diagrams Video and Example Problem Radicals     Added 03/23/02 This video also appears in the Finance collection of videos. Regression    Updated 03/23/02 Measuring the Effectiveness of a Model    Added 03/23/02 Systems Thinking    Added 03/23/02 Coefficient of Determination    Added 03/23/02 Using Regression    Updated 03/23/02 S-Curves Simulation Simulation: @RISK Reports & Graphs Slope and Y Intercept Slope: Linear Relationship for Price and Demand Straight-Line Depreciation Subscripted Variables Summation Notation Order of Operations Part I    Added 02/27/02 Part II   Added 02/27/02 Tornado Graph & Sensitivity Analysis   Video Links & Example Problems & Descriptions Alpha & Beta Errors Video and Example Problem This video discusses alpha and beta errors, statistics, decision making under risk, the Two Error Model of Classical Statistics, Type I and Type II Errors, and systems thinking. Binomial Distribution This video discusses binomial distribution, binomial formula, binomial table, discrete probability distribution, tree diagrams, spatial and symbolic thinking, cumulative and probability distributions, and Chapter 8 from The Decision Making Book. Conditional Probability This video discusses conditional probability, accuracy, and tree diagrams. Creating or Critiquing Data This video discusses creating or critiquing data, conditional probability, statistics, inductive reasoning, the logic of the data, measurement issues (accuracy, reliability, repeatability, precision), sampling (census or sample), decision making under risk, fact-based decision making, invisible numbers, fuzzy logic, and Chapter 3 from The Decision Making Book. Decision Making Process This video discusses a decision making process by examining the question, "Who will win the election: A or B?" Definitions This video is used in the @RISK Lesson on Simulation Modeling. It discusses closed and open systems, complexity, internal and external numbers, impact causing change numbers (ICCNs), uncertainty, knowledge, and Kantian knowledge. Descriptive Statistics     Updated 03/23/02 The introduction to descriptive statistics video discusses descriptive statistics (using data to create information), inferential statistics (using information to create knowledge), statistics and parameters, sample and census, constants, true average, sample average, random variable, true mean, data, standard deviation, average deviation, and Chapter 4 from The Decision Making Book. The confidence interval videos discuss the Law of Large Numbers, Central Limit Theorem, random variables, normal distribution, point estimates, statistics and parameters, interval estimates, standard deviation (level of variability), sample average, standard error of the (sample) mean, sample and census, precision, estimates and the truth, decision making under risk, and Chapters 10 and 12 from The Decision Making Book. The sample size video discusses the time and cost factors that affect sample size, along with the formula to determine it, using the level of confidence, the level of variability of the random variable, and the size of the error one can live with. The video also discusses standard deviation (which measures the variability of the random variable) and the Z value (confidence level). Descriptive Statistics Overview Videos and Example Problem    Added 06/05/01 Confidence Intervals Statistics Estimate Parameters    Added 03/23/02 Calculating Cost    Added 03/23/02 Sample Size Formula to Determine Sample Size    Added 03/23/02 Expected Value This video discusses expected value, observed averages, reasoned out averages, opinion averages, true averages, random variables, random variables of interest, mean, probability distributions, and standard deviation. Exponential Model     Added 03/23/02 This video also appears in the Finance collection of videos. Finance Formulas & Concepts    Added 03/23/02 This collection presents the mathematics used in computing simple and compound interest, present value, the annuity formula, and capital recovery. Basic vocabulary conveys sophisticated thinking to show how to work not only effectively, but also efficiently. The videos progress from stating specific formulas to developing general formulas. The videos demonstrate simplifying, recognizing patterns, and using models, formulas, and equations. They present a variety of concepts and vocabulary, such as arithmetic and geometric sequences for additive and multiplicative models, discrete and continuous mathematics, coefficients, constants, subscripted and superscripted variables, recursive formulas (displaying repetitive actions), explicit formulas ("if we use it once, we get the answer"), the common difference (using "d" to represent a constant number that is added over and over again), and the common ratio (using "r" to represent a constant number that you multiply by). This collection of Finance videos refers to a variety of additional concepts presented elsewhere in the Video Library: Slope and Y Intercept, Subscripted Variables & Summation Notation, Regression, and so on. We encourage you to study the Finance videos in the order presented below. The models provide a foundation for the formulas and equations discussed in the videos that follow. Notations used in the Finance videos: Superscripts: Some disciplines use the superscript (t) to indicate time (number of years, months, and so on); other disciplines use the superscript (n). The videos below use both references; they are interchangeable. Subscripts: A n and an mean two different things. With A n, you should sum (add) the first n terms. For A 3, you would add the first 3 terms in a sequence of terms. With an, you should find the nth term. For a3, you would find the 3rd term in a sequence of terms. Models (formulas, equations): Additive & Multiplicative Arithmetic Sequence, Part I    Added 03/23/02 Arithmetic Sequence, Part II   Added 03/23/02 Geometric Sequence, Part I    Added 03/23/02 Geometric Sequence, Part II   Added 03/23/02 Simple Interest Simple Interest Formula    Added 03/23/02 Compound Interest We are in the process of correcting the lead in video, Power of Compounding; an error appears at approximately 4:40. In the table of numbers presented, for 30 years, the value of the account should be $300,000; for 40 years, the value of the account should be $930,000. The values of the changes should be adjusted accordingly. Power of Compounding, Introduction   Added 03/23/02 Power of Compounding, Interest Rate    Added 03/23/02 Power of Compounding, Graphing    Added 03/23/02 Visualizing Compounding, Part I    Added 03/23/02 Visualizing Compounding, Part II    Added 03/23/02 Continuous Compounding, Part I    Added 03/23/02 Continuous Compounding, Part II    Added 03/23/02 Average Rate of Return    Added 03/23/02 Nominal & Effective Interest Rates    Added 03/23/02 Present Value Present Value    Added 03/23/02 Annuity Formula Annuity Formula    Added 03/23/02 Capital Recovery Factor Part I, Introduction    Added 03/23/02 Part II, Specific Formula    Added 03/23/02 Part III, General Formula    Added 03/23/02 More Models Exponents    Added 03/23/02 Radicals    Added 03/23/02 Graphing Revenue and Cost This video is used in the @RISK Lesson on Simulation Modeling. It discusses graphing revenue and cost, fixed cost, y intercept, slope of a line, marginal cost, cost function, revenue function, break even, deterministic and probabilistic models, variables, random variables, constants, decision making, simulation, @RISK software, and uncertainty. Graphing with Straight Lines: Interpret Slope, Y Intercept Inferential Statistics: See Descriptive Statistics Added 03/23/02 Kantian Knowledge This video is used in the @RISK Lesson on Simulation Modeling. It discusses definitions of closed and open systems, complexity, internal and external numbers, impact causing change numbers (ICCNs), and uncertainty. Linear Relationship for Price and Demand Mathematics: Relationships and Equations Normal Distribution This video discusses normal distribution, continuous distribution, random variable of interest, frequency diagram, histogram, standardizing, mean, and standard deviation. It shows how to use Excel to do a normal distribution formula. The video also discusses z values and the z table found in Chapter 9 in The Decision Making Book. Order of Operations Subscripted Variables Summation Notation Part I    Added 02/27/02 Part II   Added 02/27/02 These videos present the power of moving from verbal thinking (with words) to symbolic thinking (with formulas) by using the symbolic language -- algebra. They introduce basic vocabulary used with subscripted variables and summation notation to help you write and interpret symbolic statements. They also demonstrate how to translate words into symbols and symbols into words. Using this skill, you will gain efficiency in expressing problems verbally and quantitatively. To successfully solve quantitative problems you will need to know the order of operations -- what step to do first, second, and so on. The videos illustrate how to solve equations by using PERAMDAS (the order of operations -- parenthesis, exponents, radicals, absolute value, multiplication, division, addition, subtraction). Percentages Part I Part II Price and Demand, Linear Relationships Probability Using Tree Diagrams Video and Example Problem This video discusses algorithms, tree diagrams (decision trees), probability, and decision making under risk. If you are working with a problem that involves stages or steps, think about using a tree diagram. For information on software that produces tree diagrams (decision trees), go to Using Decision Analysis Software. Probability Using Venn Diagrams Video and Example Problem This video discusses Venn diagrams, categorizing, conditional probability, and targeted marketing. Radicals     Added 03/23/02 This video also appears in the Finance collection of videos. It offers a refresher in working with radicals and exponents, and relates how they are used in Finance formulas. As a refresher, it demonstrates using the calculator's "y to the x" button, following the order of operations, recognizing the impact of rounding, and the concept of "changing the form, but not the meaning." Regression    Updated 03/23/02 Measuring the Effectiveness of a Model    Added 03/23/02 Systems Thinking    Added 03/23/02 Coefficient of Determination    Added 03/23/02 Using Regression    Updated 03/23/02 These videos discuss regression, Kant (and Kantian Knowledge), knowledge, empiricists (experience), rationalists (reasoning), best fitting least squares line (BFLSL), patterns of the past and future, slope, y intercept, causation, predictions, average (unbiased estimate), error in estimating, measuring percent improvement, scattergrams, stating an addendum, and Chapter 5 from The Decision Making Book. The following concept, stated in two slightly different ways, is also discussed: Variation from the Mean Is Explained by the Model or (It Is) Not Explained Total Variation from the Mean = Total Explained Variation + Total Unexplained Variation S-Curves Simulation This video is used in the @RISK Lesson on Simulation Modeling. It discusses graphing revenue and cost, fixed cost, y intercept, slope of a line, marginal cost, cost function, revenue function, break even, deterministic and probabilistic models, variables, random variables, constants, decision making, simulation, @RISK software, and uncertainty. Simulation: @RISK Reports & Graphs This video is used in the @RISK Lesson on Simulation Modeling. It discusses Kantian and virtual knowledge, empiricists and rationalists, random variables, uncertainty, complexity, descriptive statistics (mean and standard deviation), distributions, break even, @RISK reports and graphs (Input and Output Details, Output Graph). Slope and Y Intercept Slope: Linear Relationship for Price and Demand Straight-Line Depreciation Subscripted Variables Summation Notation Order of Operations Part I    Added 02/27/02 Part II   Added 02/27/02 These videos present the power of moving from verbal thinking (with words) to symbolic thinking (with formulas) by using the symbolic language -- algebra. They introduce basic vocabulary used with subscripted variables and summation notation to help you write and interpret symbolic statements. They also demonstrate how to translate words into symbols and symbols into words. Using this skill, you will gain efficiency in expressing problems verbally and quantitatively. To successfully solve quantitative problems you will need to know the order of operations -- what step to do first, second, and so on. The videos illustrate how to solve equations by using PERAMDAS (the order of operations -- parenthesis, exponents, radicals, absolute value, multiplication, division, addition, subtraction). Tornado Graph & Sensitivity Analysis This video is used in the @RISK Lesson on Simulation Modeling. It discusses impact causing change numbers (ICCNs), break even, statistics, correlation coefficient, r value, linear relationships, random variables, simulation, and @RISK software.   Questions, Comments, and Concerns Your questions, comments, and concerns regarding these lessons are important. Please review them with your instructors. If you feel a helpline would be beneficial, please email the Site Coordinator.