Business Mathematics and Statistics KASNEB Notes

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ATD LEVEL II

COURSE OUTLINE

GENERAL OBJECTIVE

This paper is intended to equip the candidate with the knowledge, skills and attitudes that will enable him/her to apply the principles of management in practice.

LEARNING OUTCOMES

A candidate who passes this paper should be able to:

  • Apply linear, quadratic and simultaneous equations to solve business problems
  • Solve business problems using matrix algebra
  • Solve business problems involving commercial mathematics
  • Present statistical data in form of tables, graphs and curves
  • Calculate measures of location, dispersion, skewness and kurtosis
  • Apply basic probability concepts
  • Compute simple, general and weighted index numbers.

CONTENT

Equations

  • Linear equations; solving and graphs
  • Simultaneous equations; solving
  • Quadratic equations; solving and graphs
  • Basic calculus; simple differentiation and integration
  • Total revenue, total cost and profit equations
  • Break-even analysis
  • Application of errors; absolute/relative

Sequences and series

  • Arithmetic progression(A.P): nth term, sum of first n terms
  • Geometric progression (G.P): nth term, sum of first n terms

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Matrices

  • Introduction: order of matrices, types of matrices
  • Addition, subtraction and multiplication of matrices
  • Determinants of 2×2 matrices
  • Inverses of 2×2 matrices
  • Application of matrices in solving business problems

Commercial mathematics

  • Buying and selling; discounts, profit and loss, margins and mark-ups
  • Wages and salaries; piece and hourly rates, commissions, gross and net pay
  • Statutory deductions; PAYE, NHIF, NSSF
  • Simple and compound interest
  • Depreciation and appreciation of assets
  • Hire purchase
  • Foreign exchange rate transactions

Introduction to statistics

  • Introduction: definitions and branches of statistics
  • Methods of data collection: primary and secondary data,
  • Sampling techniques

Presentation of statistical data

  • Tables
  • Diagrams: bar charts and pie charts
  • Graphs: time series graphs, Z-charts, Lorenz curves and semi-logarithmic graphs
  • Frequency distribution tables
  • Histogram and frequency polygons
  • Cumulative frequency curve (ogive) and its application

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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: pearsons coefficient of skewness, product coefficient of skewness
  • Measures of kurtosis: pearsons coefficient of kurtosis, product coefficient of kurtosis.

Set theory

  • Introduction to set theory
  • Types of sets: universal, empty/null, subsets, finite and infinite
  • Operation of sets: unions, intersections, complements and set difference
  • Venn diagrams

Basic probability theory

  • Introduction to probability: definitions, events, outcomes, sample space
  • Types of events: simple, compound, independent, mutually exclusive, mutually inclusive, dependent events
  • Rules of probability: additive and multiplicative rules
  • Introduction to counting techniques, combinations and permutations
  • Baye’s Theorem
  • Elementary probability trees

Index numbers

  • Construction of index numbers
  • Purpose of index numbers
  • Simple index numbers; fixed base method and chain base method
  • Weighted index numbers; Laspeyre’s, Paasche’s, Fisher’s ideal and Marshall- Edgeworth’s methods (both price and quantity index numbers)
  • Consumer Price Index (CPI)
  • Applications of CPI
  • Limitations of index numbers

Emerging issues and trends

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