**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.

**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

### 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

### Matrices

- Introduction: order, types
- Addition, subtraction and multiplication
- 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

### Collection and presentation of data

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

### Descriptive statistics

– Measures of central tendency: mean: arithmetic mean, weighted arithmetic mean; median, mode, geometric mean and harmonic mean

- 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