# Business Mathematics and Statistics KASNEB Notes 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:

• 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.

### 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

### 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

## 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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