Introduction to Quantitative Analysis: A Comprehensive Guide for Decision-Making | Study notes Quantitative Techniques

CHAPTER 1: INTRODUCTION TO QUANTITATIVE ANALYSIS

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:

1) Central Tendency: This technique provides us with an estimation of the

concentration of the values of the central part of a certain distribution. There

are five methods of finding this out✔✔

● Arithmetic Mean or Simple Mean

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CHAPTER 1: INTRODUCTION TO QUANTITATIVE ANALYSIS

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:

Central Tendency: This technique provides us with an estimation of the concentration of the values of the central part of a certain distribution. There are five methods of finding this out✔✔ ● Arithmetic Mean or Simple Mean

● Mode ● Geometric Mean ● Harmonic Mean ● Median

Dispersion✔✔Literal meaning of dispersion is “Scatteredness.”According to statistician, Spiegel, dispersion or variation is defined as “the degree to which the nu merical data tend to spread about an average value.” Dispersion can be measured in different ways: ✔✔ ● Mean Deviation ● Range ● Standard Deviation and Variation ● Quartile Deviation
Skewness: ✔✔ Skewness means ‘Lack of symmetry.’ The study of skewness is done to understand how to shape the curve with a given data. The data can be said to have positive skewness, negative skewness, and zero skewness.
Kurtosis: ✔✔ Kurtosis enables us to understand the ‘peakedness or flatness’ of the curve when formed from a given set of data. Correlation and Regression Analysis: Linear relationship amongst two or more variables can be analysed with the help of Correlation. Whereas, usage of a variable is used for estimation of value of another variable under regression. c) Correlation and Regression Analysis: ✔✔Linear relationship amongst two or more variables can be analysed with the help of Correlation. Whereas, usage of a variable is used for estimation of value of another variable under regression. d) Index Numbers: ✔✔ Rightfully described as economic barometers, these numbers allow us to measure and analyze the fluctuations of various things such as price, production and various other things, for a given time period. It is because of its ability to give results for fluctuations; Index Numbers is an integral part of Statistics. e) Time Series Analysis: ✔✔This technique is used for understanding regarding effects of factors, which are responsible for a change during a given period. f) Interpolation and Extrapolation: ✔✔Interpolation is a statistical technique, which is used for estimation of particular things under assumptions for missing statistics that fall within the range of given figures. On the other hand, for estimated figures, which fall outside range of a given data, are Extrapolation is used. g) Statistical Quality Control: ✔✔ it is an industrial standard, which is used to measure the quality of goods and services. It can also be used for measuring as well con trolling the quality of services. Various charts are employed for calculations related to product quality. h) Ratio Analysis: ✔✔ it is a method used for analysis of financial statements and evaluates the industrial aspects of the company, business or industry. It also helps in com paring two data in different units. i) Probability Theory: ✔✔ It assigns numerical values of the prospective of an event reoccurring.

(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

Introduction to Quantitative Analysis: A Comprehensive Guide for Decision-Making, Study notes of Quantitative Techniques

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CHAPTER 1: INTRODUCTION TO QUANTITATIVE ANALYSIS