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.
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.
5.1 Mathematical Techniques
- Functions, equations, inequalities and graphs; linear, quadratic, cubic, exponential and logarithmic
- Application of mathematical functions in solving business problems
5.1.2 Matrix Algebra
- Types and operations (addition, subtraction, multiplication, transposition and inversion of up to order 3×3)
- Application of matrices; statistical modelling, Markov analysis, input-output analysis and general applications
- 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
- Rules of integration (general rule)
- Integration of exponential and logarithmic functions
- Applications of integration to business problems
- 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.
5.3.1 Set Theory
- 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
5.3.2 Probability Theory and Distribution
- 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
5.3.3 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
- 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
5.5 Correlation and Regression Analysis
5.5.1 Correlation Analysis
- Scatter diagrams
- Measures of correlation – product-moment and rank correlation coefficients (Pearson and Spearman) using R software
5.5.2 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
5.6 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
5.7 Decision Theory
- 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
- Decision making under uncertainty – maximin, maximax, minimax regret, Hurwicz decision rule, Laplace decision rule.
Dubey, U., Kothari, D. P., & Awari, G. K. (2016). Quantitative techniques in business, management and finance: A case-study approach. CRC Press.
Taha, H. A. (2017). Operations research an introduction. © Pearson Education Limited 2017.
Groebner, D. F., Shannon, P. W., Fry, P. C., & Smith, K. D. (2013). Business statistics. Pearson Education UK.
Berenson, M., Levine, D., Szabat, K. A., & Krehbiel, T. C. (2012). Basic business statistics: Concepts and applications. Pearson higher education AU.