# BUSINESS MATHEMATICS AND STATISTICS REVISION KIT – ATD 2 QUESTION AND ANSWER

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KASNEB SYLLABUS

PAPER NO. 7 BUSINESS MATHEMATICS AND STATISTICS

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.

7.0 LEARNING OUTCOMES

A candidate who passes this paper should be able to:

• 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

7.1 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

7.2 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

7.3 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

7.4 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

7.5 Introduction to statistics

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

7.6 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

7.7 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.

7.8 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

7.9 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

7.10 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

7.11 Emerging issues and trend

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