PAPER NO. 5 QUANTITATIVE ANALYSIS
UNIT DESCRIPTION
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.
LEARNING OUTCOMES
A candidate who passes this paper should be able to:
 Use mathematical techniques to solve business problems.
 Apply set and probability theories in business decision making
 Apply operation research techniques in decision making
 Apply hypothesis testing in analysing business situations
 Apply linear programming to solve practical business problems
CONTENT

Mathematical Techniques
 Functions
 Definition
 Functions, equations, inequalities and graphs; linear, quadratic, cubic,Exponential and logarithmic functions
 Application of mathematical functions in solving business problems
 Functions
 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
 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

Probability
 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 and Distribution
 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 chisquare)
 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
 ChiSquare tests of goodness of fit and independence
 Hypothesis testing using R statistical software

Correlation and Regression Analysis

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, semiaverages, moving averages, leastsquares 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)
8. Decision Theory

 Definition
 Decisionmaking process
 Decisionmaking 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
 Decision making under uncertainty – maximin, maximax, minimax regret, Hurwicz decision rule, Laplace decision rule.
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KASNEB elibrary
KASNEB elibrary