CPA 005: Quantitative Analysis - Globopoint Learning Centre

About Course

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GENERAL OBJECTIVE

This paper is intended to equip the candidate with knowledge, skills, and attitudes that will enable the learner to use quantitative analysis tools in business operations and decision-making.

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Course Content

FUNCTIONS

Definition

04:43
Functions, equations, inequalities and graphs; linear, quadratic, cubic, Exponential and logarithmic functions

31:30
Application of mathematical functions in solving business problems

18:48
Sample Questions

34:37

MATRIX ALGEBRA

CALCULUS-DIFFERENTIATION

CALCULUS-INTEGRATION

DESCRIPTIVE STATISTICS

SET THEORY

PROBABILITY THEORY

PROBABILITY DISTRIBUTIONS

HYPOTHESIS TESTING AND ESTIMATION

CORRELATION ANALYSIS

REGRESSION ANALYSIS

TIME SERIES

LINEAR PROGRAMMING

DECISION THEORY

WORKED OUT QUESTIONS

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About Course

Book a Course Recap Zoom Session

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What Will You Learn?

Course Content

FUNCTIONS

Definition

Functions, equations, inequalities and graphs; linear, quadratic, cubic, Exponential and logarithmic functions

Application of mathematical functions in solving business problems

Sample Questions

MATRIX ALGEBRA

Definition

Types and operations (addition, subtraction, multiplication, transposition and inversion of up to order 3×3)

Application of matrices; statistical modelling, Markov analysis, inputoutput analysis and general applications

CALCULUS-DIFFERENTIATION

Definition

Rules of differentiation (general rule, chain, product, quotient)

Differentiation of exponential and logarithmic functions

Turning points (maxima, minima and inflexion)

Application of differentiation to business problems

CALCULUS-INTEGRATION

Definition

Rules of integration (general rule)

Integration of exponential and logarithmic functions

Applications of integration to business problems

DESCRIPTIVE STATISTICS

Measures of central tendency: mean: arithmetic mean, weighted arithmetic mean; geometric mean, harmonic mean, median and mode

Measures of dispersion: range, quartile, deciles, percentiles, mean deviation, standard deviation and coefficient of variation

Measures of skewness: Pearson’s coefficient of skewness, product coefficient of skewness

Measures of kurtosis: Pearson’s coefficient of kurtosis, product coefficient of kurtosis

SET THEORY

Set Theory

Definition

Types of sets

Set description; enumeration and descriptive properties of sets

Venn diagrams (order – Venn diagrams precede operation of sets)

Operations of sets; union, intersection, complement and difference

PROBABILITY THEORY

Definitions; event, outcome, experiment, sample space, probability space

Types of events: elementary, compound, dependent, independent, mutually exclusive, exhaustive, mutually inclusive

Laws of probability; additive and multiplicative laws

Conditional probability and probability trees

Expected value, variance, standard deviation and coefficient of variation using frequency and probability

Application of probability and probability distributions to business problems

PROBABILITY DISTRIBUTIONS

Discrete and continuous probability distributions Z, F, test statistics (geometric, uniform, normal, t distribution, binomial, Poisson and exponential and chi-square)

Application of probability distributions to business problems

HYPOTHESIS TESTING AND ESTIMATION

The arithmetic mean and standard deviation

Hypothesis tests on the mean (when population standard deviation is unknown)

Hypothesis tests on proportions

Hypothesis tests on the difference between two proportions using Z and t statistics

Chi-Square tests of goodness of fit and independence

Hypothesis testing using R statistical software

CORRELATION ANALYSIS

Scatter diagrams

Measures of correlation – product-moment and rank correlation coefficients (Pearson and Spearman) using R software

REGRESSION ANALYSIS

Simple and multiple linear regression analysis

Assumptions of linear regression analysis

Coefficient of determination, standard error of the estimate, standard error of the slope, t and F statistics

TIME SERIES

Definition of time series

Components of time series (circular, seasonal, cyclical, irregular/ random, trend)

Application of time series

Methods of fitting trend; freehand, semi-averages, moving averages, least-squares methods

Models – additive and multiplicative models

Measurement of seasonal variation using additive and multiplicative models

Forecasting time series value using moving averages, ordinary least squares method and exponential smoothing

LINEAR PROGRAMMING

Definition of decision variables, objective function and constraints

Assumptions of linear programming

Solving linear programming using graphical method

Solving linear programming using simplex method (basic scenarios)

DECISION THEORY

Definition

Decision-making process

Decision-making environment; deterministic situation (certainty)

Decision making under risk – expected monetary value, expected opportunity loss, risk using the coefficient of variation, the expected value of perfect information

Decision trees – sequential decision, the expected value of sample information