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A comprehensive introduction to quantitative analysis, a scientific approach to managerial decision-making. It explores various quantitative techniques based on mathematical, statistical, and programming principles. The document delves into key concepts like data collection, statistical calculations, and model building techniques, offering practical examples and applications. It also highlights the importance of defining problems, developing models, acquiring input data, and implementing solutions in a quantitative analysis framework.
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Quantitative Analysis ✔✔scientific approach to managerial decision-making in which raw data are processed and manipulated to produce meaningful information Quantitative Factors ✔✔are data that can be accurately calculated Qualitative Factors ✔✔are more difficult to quantify but affect the decision process Classes of Quantitative Techniques✔✔ a) Quantitative Techniques based on mathematical calculations b) Quantitative Techniques based on statistical calculations c) Quantitative Techniques based on programming Quantitative Techniques based on mathematical calculations✔✔ The techniques that use mathematical principles to analyze the quantitative data includes: a) Combinations and Permutations✔✔ The term “permutation” implies the possible representation of the various items that have been selected in an order. The total number of the arrangements in the order is and will be directly proportional to the total quantity of items used at the time of creation of the order. Combination focuses on selecting the objects without considering the order in which they are selected. b) Set Theory✔✔Set theory is a branch of quantitative techniques which deals with the collection of objects. c) Matrix Algebra✔✔ A matrix can be described as representation of particular variables and numbers in different columns and rows. Matrix is a mathematical tool that is used to identify different types of algebra calculations by making use of the numbers and variables given in the various rows and columns. d) Determinants✔✔ It is a useful value that can be computed from the elements of a square matrix. Apart from its application in calculus, it can also be used to represent complex polynomial in a simpler form. e) Differentiation: ✔✔Differentiation is a complex mathematical operation which allows you to find out the results of a minor change in an independent variable on a dependent variable in the equation. f) Integration✔✔Integration can be defined as the converse procedure of differentiation. g) Differential Equation✔✔ It is a mathematical equation that encompasses the differential factors of the dependent variables. Quantitative Techniques based on statistical calculations includes✔✔ a) Collection of Data✔✔ It is the first and foremost step for any statistical method. Primary and secondary data collection involves varied techniques. b) Measures of Dispersion, Kurtosis, Central Tendency, and Skewness:
● Mode ● Geometric Mean ● Harmonic Mean ● Median
(b) Statistical details of records for upkeep of a vast market. (c) Sales planning and projections. (ii) Production: (a) Controlling and planning production. (b) Performance evaluation of a machine. (c) Requirements for control of quality. (d) Measures for Inventory control. (iii) Accounting, Investment and Finance: (a) Preparing budgets and forecasting about financial performance. (b) Decisions regarding financial investment. (c) Securities selection. (d) Carrying out Audit. (e) Credit policies, delinquent accounts and credit risk. iv) Personnel: (a) Turnover rate of Labour. (b) Trends regarding employment. (c) (c) Appraisal of Performance. (d) (d) Rates of wages and plans for incentives. The Quantitative Analysis Approach ✔✔ (1) Defining the Problem, (2) Developing a Model, (3) Acquiring Input Data, (4) Developing a Solution, (5) Testing the Solution, (6) Analyzing the Results, (7) Implementing the Results Defining the Problem ✔✔develop a clear and concise statement that gives direction and meaning to subsequent steps Developing a Model ✔✔quantitative analysis models are realistic, solvable and understandable mathematical representations of a situation What are the different types of models? ✔✔Scale Models Schematic Models What kind of variables to models contain? ✔✔Controllable and Uncontrollable Controllable Variables ✔✔decision variables and are generally unknown Acquiring Input Data ✔✔Data may come from a variety of sources such as company reports, company reports, company documents, interviews, on-site direct measurement or statistical sampling.
Input data must be accurate-GIGO rule. What is the GIGO rule? ✔✔Garbage In Process Garbage Out Developing a Solution ✔✔the best solution to a problem is found by manipulating the model variables until solutions is found that is practical and can be implemented What are the common techniques to developing a solution? ✔✔Solving equations Trial and error- trying various approaches and picking the best results Complete enumeration- trying all possible values Using an algorithm- a series of repeating steps to reach a solution Testing the Solution ✔✔both, input data and the model should be tested for accuracy before analysis and implementation Analyzing the Results ✔✔Determine the implications of the solution: Implementing results often requires change in an organization The impact of actions or changes needs to be studied and understood before implementation Sensitivity Analysis ✔✔determines how much the results will change if the model or input data changes Implementing the Results ✔✔Implementation incorporates the solution into the company: Implementation can be very difficult People may be resistant to changes Many quantitative analysis efforts have failed because a good, workable solution was not properly implemented Mathematical Model of Profit ✔✔Profit= Revenue-Expenses Profit Equation ✔✔Revenue- (Fixed Cost+ Variable Cost) (Selling price per unit)(Number of units sold)-[Fixed Cost+ (Variable costs per unit)(Number of units sold)] Profit Equation (2) ✔✔Profit = sX-[f+vX] Profit= sX-f-vX s= selling price per unit v= variable cost per unit f= fixed cost X= number of units sold