# Syllabus of O5 Business Mathematics and Statistical Inference

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## Detailed Syllabus Contents:

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PART – A

1. Basic Mathematical Techniques

• Integers, Fractions and Decimals
• Order of Operations
• Percentage and Ratios
• Roots and Powers
• Errors

2. Formulae and Equations

• Introduction
• Manipulating Inequalities
• Linear Equations, Linear Equations and Graphs, Simultaneous Equations
• Non-Linear Equations, Progressions
• Arithmetic Progression
• Geometric Progression (nth Terms and Sum)
• Matrices (Definition Sum and multiplication of two matrices)
• Use in Solving simultaneous, equators, Cramer’s rules
• Linear programming, Properties and using of programming for maximization of profit and minimization of cost.

3. Derivatives

• Concept of Derivative and differentiation
• Basic Rules of differentiation
• Instantaneous rate of change
• Derivatives, Maxima and Minima & Point of Inflection

4. Compounding and Discounting

• Simple Interest, Compound Interest, Equivalent Rates of Interest
• Regular Savings and Sinking Funds
• Loan and Mortgages
• Concept of Discounting

5. Basic Investment Appraisal

• Net Present Value (NPV) Method
• Internal Rate of Return (IRR) Method
• Annuities and Perpetuities
• Using Spreadsheet(Define Spread sheet, need to use of spread sheet, Define work book, work sheets and type of cell contents)
• Shareholder Value(define shareholder value and identify financial objectives to maximize shareholders wealth)

PART – B

STATISTICS AND STATISTICAL INFERENCE

6. Data and Information

• Introduction, Characteristics of Good Information, Data Type (Qualitative and Quantitative data, primary and secondary data, discrete and continuous data)

7. Collection and Presentation of data

• Tables, Charts, Frequency Distribution, Histograms, Ogives, Scatter Diagram

8. Averages

• Arithmetic Mean, Harmonic mean, Geometric mean, Mode, Median

9. Dispersion

• Range
• Quartiles and Quartile Range and Quartile deviation orthe Semi-Quartiles Range
• Mean Deviation
• Variance and Standard Deviation
• Coefficient of Variation
• Skewness

10. Correlation and Linear Regression

• Correlation
• Correlation Coefficient and Coefficient of determination
• Spearman’s Rank Correlation Coefficient
• Lines of Best Fit
• Scatter Graph Method
• Linear Regression Analysis

11. Index numbers

• Basic Terminology
• Index Relatives
• Time Series of Index Relatives
• Time Series Deflation
• Composite Index Numbers
• Weighted Index Numbers
• Retail Price Index for Pakistan

12. Probability

• Concept of Probability and counting techniques (including multiplication rules of counting, combinations, permutations, etc))
• Rules of Probability
• Expected Values
• Expectation and Decision Making

13. Normal distribution

• Probability Distributions(Discrete and continuous)
• Normal Distribution
• Standard Normal Distribution
• Binominal of passion distribution
• Hyper geometric distribution
• Using Normal Distribution to Calculate Probabilities
• Pareto Distribution and 80:20 Rule

14. Estimation & Testing

• Confidence Interval Z and T test for single population mean
• Testing hypothesis Z and T test for single population mean
• Chai square distribution

15. Sampling & Sampling Frequency Distribution

• Sampling Frequency Distribution with & without replacement for sample size 2 and 3
• Random and Non-Random Sampling
• Sampling Frequency distribution for proportion

16. Forecasting – Time series

• Components of Time Series (Define time series and identify its examples, preparing time series graphs and identifying trends)
• Finding the Trend (Methods, prepare trend equation using graphical means or regression analysis)
• Finding the Seasonal Variations (Define Season variations, finding the seasonal components using additive and multiplicative models)
• Forecasting (Define forecasting, forecasting using linear regression analysis)

Limitation of Forecasting Models

## syllabus of O5 Business Mathematics and Statistical Inference:

syllabus of O5 Business Mathematics and Statistical Inference syllabus of O5 Business Mathematics and Statistical Inference syllabus of O5 Business Mathematics and Statistical Inference syllabus of O5 Business Mathematics and Statistical Inference syllabus of O5 Business Mathematics and Statistical Inference