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

5.1.1 Functions

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


5.1.2 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, input-output analysis and general applications




  • 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



  • 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.




5.3.1 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


5.3.2 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


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

  •  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
  • Decision making under uncertainty – maximin, maximax, minimax regret, Hurwicz decision rule, Laplace decision rule.


Reference Texts


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.

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