# Quantitative Methods

## Overview

Many business problems cannot be solved without the use of mathematical methods. All businesses collect masses of data during the course of their daily activities. This data must be organised and analysed in such a way that all of the key decision-making staff can make sense of it.

Data collection requires techniques which are often sophisticated. Collected data must then be analysed; the business must have some idea of the meaning of their data. The data can be used to diagnose the problems faced by the business.

When business problems have been diagnosed, then a whole range of techniques (many of them mathematical) can be used to help provide solutions to problems. This is why this course is inevitably concerned with the techniques used for problem solving.

But as you will see from the above, the concern does not just end at the use of the technique, it extends back to the collection of the data required by the technique, and the inevitable questions raised about whether the correct methods are being used.

The importance of the above is to prevent you from making the mistake of thinking that QM will merely consist of a set of techniques. Techniques are important, but the reasons why we use them, and the degree of success we can expect from them are much more important.

**Overview**

Analysis and organisation of data acquired during the course of a business's daily activities, using mathematical methods, so that all key decision-making staff can make sense of it and apply it to problem-solving.

## Modules

**UNIT ZERO - BASIC MATHS**

Unit Objectives

Section 1. Numbers

1. Our Number System

2. The Number Line

3. Counting Numbers

4. Parts of Counting Numbers

5. Rounding

6. Comparisons of Numbers

7. Percentages

8. Summary

Section 2 Algebra

1. Letters for Numbers

2. Indices, Powers and Exponents

3. Basic Rules for Products Involving Indices

4. Sequence of Operations

5. Directed (or Signed) Numbers

6. Manipulating Arithmetic Fractions

7. Multiplication and Division in Algebra

8. Use of Brackets

9. Summary

Section 3 Equations and Coeffecicients

1. Simple Equations

2. Changing the Subject of a Formula

3. Simultaneous Equations

4. Expanding Brackets

5. Coefficients

6. Inequalities

7. Summary

Section 4 Using a Calculator

1. Basic Calculations

2. The Square Root Function

3. The Square Function

4. The General Power Function

5. The Factorial Function

6. The Scientific Notation

7. Use of the Memory Facility

8.Combination of Functions

9. Summary

**UNIT ONE - BUSINESS MATHS**

Section 1 Financial Analysis

1. Interest Rates

2. Number Patterns

2.1 Pattern 1. Arithmetric Progressions

2.2 Pattern 2. Geometric Progressions

2.3 Pattern 3. Summing the Terms of a Geometric Progression

3. Calculation of Interest Earned

4. Notation

5. Compound Interest

6. A More General Approach to Interest

7. Applying the General Result to Particular Cases

8. Comparison of Interest Rates

9. Present Value of a Future Sum

10. Financially Equivalent Sums

11.Summary

12. Repaying a Loan

12.1 Calculating the Amount of a Loan

12.2 Calculating the Repayments

12.3 Loan Repayment Schedules

12.4 Mortgages

12.5 Annuities

13. Investment Decisions

14. Regular Savings Seach Schemes

14.1 Calculating the Value of a Scheme

14.2 Calculating the Sum to Achieve a Given Valuation

15. Summary

Section 2 Graphs

1. The Grid System

2. Straight Line Graphs

2.1 Straight Lines From an Equation

2.2 Slope of a Line

2.3 The Equation of a Straight Line

2.4 Detailed Inspection of the Equation

2.5 Other Forms of the Equation

2.6 Comparative Slopes

2.7 Summary

3. Other Graphs

4. Summary

**UNIT TWO - DATA PRESENTATION**

Section 1 Data, Variables and Measurement

1. What is Statistics

2. Measurement

3. Elements, Variables and Data

4. Summary

Section 2 The Frequency Distribution

1. Data, Frequencies Classes and Distributions

2. Frequency Distributions and Variability

3. How to Construct a Frequency Distribution

4. Frequency Distributions and Diagrams

5. Note for Computer Users

6. Types of Distribution

7. Summary

Section 3 Measures of Central Tendency

1. Introduction: Summary Statistics

2. What Are Measures of Central Tendency?

3. The Arithmetic Mean

4. The Mean of a Grouped Frequency Distribution

5. The Median

6. Calculating The Median for Grouped Data

7. The Mode

8. Summary

Section 4 Understanding Averages

1. What Kind of Variable are we Dealing With?

2. How Representative is the Measure of Central Tendency?

3. How are the Data Distributed?

4. Quick Estimate or Thorough One?

5. Do We Plan to Carry Out Further Analysis?

6. Summary

Section 5 Measures of Dispersion or Variation

1. Why Measure Variability?

2. How Can We Measure Variability?

3. Calculating s2 and s For Frequency Data

4. Summary

Section 6 Interpreting the Variance and Standard Deviation

1. Why Do we need the Standard Deviation?

2. Comparing Two or More Sets of Data

3. Chebyshev's Theorem

4. Symmetrical or Bell-Shaped Distributions

5. Z-Scores (Standard Scores)

6. Summary

References

Glossary

**UNIT THREE - LINEAR PROGRAMMING**

Unit Objectives

Section 1: A Case Study

1. Introduction: A Linear Programming Problem

2. What Does Linear Programming Do?

3. Applications of Linear Programming

4. Jarvis & Partners: Developing a Model

5. Summary

Section 2: Developing a Linear Programming Model

1. Introduction

2. Linear Equations and Linear Inequalities

3. More Case Studies

4. Summary

Section 3: Solving Linear Programming Problems Using Graphical Methods

1. Introduction

2. Jarvis Builders Revisited

3. Summary

Section 4: Practising the Graphical Solution Technique

1. Introduction

2. Superb Audio plc: a Graphical Solution

3. The Small Mine: a Graphical Solution

4. Rest Easy Lounge Suites: a Graphical Solution

5. The Doll's Workshop: a Graphical Solution

6. Summary

Section 5: Shadow Prices and Sensitivity Analysis

1.Introduction

2. Scarce Resources and Shadow Prices

3. Calculating Shadow prices

4. Shadow Prices and Sensitivity

5. Summary

Section 6: The Role of Computer Software

1. Introduction

2. The Simplex Algorithm

3. Simplex Linear Programming - Sample Output

4. More Than Two Decision Variables

5. Limitations of Linear Programming

6. Summary

References

Glossary

**UNIT FOUR - REGRESSION AND CORRELATION**

Unit Objectives

Section 1. Relationships Between Variables

1. What is Correlation and Regression?

2. Relationships Between Variables

3. Summary

Section 2. The Coefficient of Correlation

1. Correlation Between Variables

2.The Coefficient of Correlation

3.Interpretation of the Coefficient of Correlation

4. Summary

Section 3. Interpreting the Coefficient of Correlation

1. Linearity

2. Causality

3. Trends

4. Sample Size and Accuracy

5. Non-Ratio Scale Data

6. Summary

Section 4. Regression Analysis

1. What is Regression Analysis

2. The Purpose of Regression

3. Finding the Form of the Regression Equation

4. Best Fit - The Least Squares Method

5. Statistical and Spreadsheet Packages

6. Dependent and Independent Variables

7. Summary

Section 5. How Effective is Regression Analysis?

1. What We Have Accomplished So Far

2. Interpretation of the Coefficient of Determination

3. Summary

Section 6. What Next?

1 Where Do We Go From Here?

2. Correlation, Regression and Non-Ratio Scale Data

3. Dealing With a Time Series

4. What Can We Do About Non-Linearity?

5. Must We Always Be Limited to Two Variables?

6. Summary

References

Glossary

**UNIT FIVE - PROBABILITY**

Unit Objectives

Section 1. The Problem of Measurement

1. Introduction

2. What is Probability

3. Percentages and Odds

4. Summary

Section 2. Events, contingency Tables and Venn

Diagrams

1. Simple and Complex Events

2. Probability Notation and Venn Diagrams

3. Summary

Section 3. Rules for Calculating Probabilities

1. Introduction

2. Conditional Probabilities

3. The Intersection of Events

4. The Union of Events

5. Complementary Events

6. Summary

Section 4. Putting the Rules of Probability to Work

1. Introduction

2. Summary

Section 5. Probability Trees

1. Introduction

2. Probability Trees in Use

3. Summary

Section 6. Counting Techniques

1. Introduction

2. The 'MN' Rule

3. The Permutations Rule

4. The Combinations Rule

5. Summary

References

Glossary

**UNIT SIX - PROBABILITY DISTRIBUTION**

Unit Objectives

Section 1. Random Variables

1. Introduction

2. Discrete and Continuous Variables

3. Probability and Random Variables

4. Probability Distributions

5. What Do Probability Distributions Look Like?

6. Conclusion

7. Summary

Section 2. Mathematical Functions of Probability Distributions

1. Introduction

2. Functions and Discrete Data

3. Functions and Continuous Data

4. Conclusion

5. Summary

Section 3. Summing Up Probability Distributions

1. Introduction

2. Expected Value For a Discrete Variable

3. The Variance of a Discrete Random Variable

4. Expected Value and Variance: Continuous Variables

5. Interpretation of Expected Value and Variance

6. Summary

Section 4. Binomial Distribution

1. Introduction: A Matter of Insurance

2. The General Form of the Binomial Distribution

3. Expected Value and Variance of a Binomial Distribution

4. Summary

Section 5. Normal Distribution

1. Introduction

2. Characteristics of the Normal Distribution

3. Mean and Standard Deviation of the Normal Distribution

4. Probability and Areas Under the Normal Curve

5. The Standard Normal Distribution

6. Summary

Section 6. Using the Normal Distribution

1. Non-Standard Normal Distributions

2. The Normal Curve and Binomial Probabilities

3. Summary

4. Unit Summary and Conclusions

References

Glossary

Tables of Areas Under the Standard Normal Curve

**UNIT SEVEN - INTRODUCTION TO SAMPLING**

Unit Objectives

Section 1 Sample and Population

1. Introduction

2. Random Sampling

3. Selecting a Random Sample

4. Can We Trust Sample Estimates?

5. Summary

Section 2 The Behaviour of Sample Estimates

1. Terminology

2. The Central Limit Theorem

3. Summary

Section 3 Point Estimates and Interval Estimates

1. Problems in Estimation

2. Calculation of Interval Estimates

3. Interpretation of Confidence Intervals

4. How Precise Are Interval Estimates?

5. How Precise Are Sample Estimates?

6. Summary

Section 4 Proportions and Percentages

1. Introduction

2. Sampling Distribution of Proportions

3. Confidence Intervals for Proportions

4. Summary

Section 5 Sample Size Problems

1. Introduction

2. Deciding Sample Size: The Method

3. Proportions and Sample Size Problems

4. Summary

Section 6 Significance Testing

1. Introduction

2. Construction of Statistical Tests

3. Possible Mistakes in Statistical Tests

4. Notes Concerning the Use of Sampling Theory

5. Summary

References

Glossary

Table of Areas Under the Standard Normal Curve

**UNIT EIGHT - INDEX NUMBERS**

Unit Objectives

Section 1 The Measurement of Change

1. Why Measure Change?

2. Simple Index Numbers

3. More Complex Index Numbers

4. The Price Relative Method

5. Summary

Section 2 Weighted Indices and Aggregative Methods of Calculation

1. Weighted Index Numbers

2. Selecting Suitable Weights

3. The Aggregative Method of Calculation

4. Summary

Section 3 Quantity and Value Indices

1. Value and Volume Indices

2. Using a Value Index as a Deflater

3. The UK Retail Prices Index

4. Summary

Section 4 Time Series

1. Introduction

2. A Sales Data Time Series

3. Breaking Down a Time Series

4. Models of Time Series Data

5. Summary

Section 5 Moving Averages

1. Introduction

2. Moving Averages

3. Seasonal Variation

4. Summary

Section 6 Forecasting a Time Series

1. Using Regression Analysis on a Time Series

2. The Multiplicative Model

3. Summary

References

Glossary

## Requirements

There is no experience or previous qualifications required for enrolment on this course. It is available to all students, of all academic backgrounds.

## Assessment

**Assessment Method**

After each lesson there will be a question paper, which needs to be completed and submitted to your personal tutor for marking. This method of continual assessment ensures that your personal tutor can consistently monitor your progress and provide you with assistance throughout the duration of the course.

**What's Included**

- All study materials
- Study Guide
- Full Tutor and Admin support

Many business problems cannot be solved without the use of mathematical methods. All businesses collect masses of data during the course of their daily activities. This data must be organised and analysed in such a way that all of the key decision-making staff can make sense of it.

Data collection requires techniques which are often sophisticated. Collected data must then be analysed; the business must have some idea of the meaning of their data. The data can be used to diagnose the problems faced by the business.

When business problems have been diagnosed, then a whole range of techniques (many of them mathematical) can be used to help provide solutions to problems. This is why this course is inevitably concerned with the techniques used for problem solving.

But as you will see from the above, the concern does not just end at the use of the technique, it extends back to the collection of the data required by the technique, and the inevitable questions raised about whether the correct methods are being used.

The importance of the above is to prevent you from making the mistake of thinking that QM will merely consist of a set of techniques. Techniques are important, but the reasons why we use them, and the degree of success we can expect from them are much more important.

**Overview**

Analysis and organisation of data acquired during the course of a business's daily activities, using mathematical methods, so that all key decision-making staff can make sense of it and apply it to problem-solving.

## Modules

**UNIT ZERO - BASIC MATHS**

Unit Objectives

Section 1. Numbers

1. Our Number System

2. The Number Line

3. Counting Numbers

4. Parts of Counting Numbers

5. Rounding

6. Comparisons of Numbers

7. Percentages

8. Summary

Section 2 Algebra

1. Letters for Numbers

2. Indices, Powers and Exponents

3. Basic Rules for Products Involving Indices

4. Sequence of Operations

5. Directed (or Signed) Numbers

6. Manipulating Arithmetic Fractions

7. Multiplication and Division in Algebra

8. Use of Brackets

9. Summary

Section 3 Equations and Coeffecicients

1. Simple Equations

2. Changing the Subject of a Formula

3. Simultaneous Equations

4. Expanding Brackets

5. Coefficients

6. Inequalities

7. Summary

Section 4 Using a Calculator

1. Basic Calculations

2. The Square Root Function

3. The Square Function

4. The General Power Function

5. The Factorial Function

6. The Scientific Notation

7. Use of the Memory Facility

8.Combination of Functions

9. Summary

**UNIT ONE - BUSINESS MATHS**

Section 1 Financial Analysis

1. Interest Rates

2. Number Patterns

2.1 Pattern 1. Arithmetric Progressions

2.2 Pattern 2. Geometric Progressions

2.3 Pattern 3. Summing the Terms of a Geometric Progression

3. Calculation of Interest Earned

4. Notation

5. Compound Interest

6. A More General Approach to Interest

7. Applying the General Result to Particular Cases

8. Comparison of Interest Rates

9. Present Value of a Future Sum

10. Financially Equivalent Sums

11.Summary

12. Repaying a Loan

12.1 Calculating the Amount of a Loan

12.2 Calculating the Repayments

12.3 Loan Repayment Schedules

12.4 Mortgages

12.5 Annuities

13. Investment Decisions

14. Regular Savings Seach Schemes

14.1 Calculating the Value of a Scheme

14.2 Calculating the Sum to Achieve a Given Valuation

15. Summary

Section 2 Graphs

1. The Grid System

2. Straight Line Graphs

2.1 Straight Lines From an Equation

2.2 Slope of a Line

2.3 The Equation of a Straight Line

2.4 Detailed Inspection of the Equation

2.5 Other Forms of the Equation

2.6 Comparative Slopes

2.7 Summary

3. Other Graphs

4. Summary

**UNIT TWO - DATA PRESENTATION**

Section 1 Data, Variables and Measurement

1. What is Statistics

2. Measurement

3. Elements, Variables and Data

4. Summary

Section 2 The Frequency Distribution

1. Data, Frequencies Classes and Distributions

2. Frequency Distributions and Variability

3. How to Construct a Frequency Distribution

4. Frequency Distributions and Diagrams

5. Note for Computer Users

6. Types of Distribution

7. Summary

Section 3 Measures of Central Tendency

1. Introduction: Summary Statistics

2. What Are Measures of Central Tendency?

3. The Arithmetic Mean

4. The Mean of a Grouped Frequency Distribution

5. The Median

6. Calculating The Median for Grouped Data

7. The Mode

8. Summary

Section 4 Understanding Averages

1. What Kind of Variable are we Dealing With?

2. How Representative is the Measure of Central Tendency?

3. How are the Data Distributed?

4. Quick Estimate or Thorough One?

5. Do We Plan to Carry Out Further Analysis?

6. Summary

Section 5 Measures of Dispersion or Variation

1. Why Measure Variability?

2. How Can We Measure Variability?

3. Calculating s2 and s For Frequency Data

4. Summary

Section 6 Interpreting the Variance and Standard Deviation

1. Why Do we need the Standard Deviation?

2. Comparing Two or More Sets of Data

3. Chebyshev's Theorem

4. Symmetrical or Bell-Shaped Distributions

5. Z-Scores (Standard Scores)

6. Summary

References

Glossary

**UNIT THREE - LINEAR PROGRAMMING**

Unit Objectives

Section 1: A Case Study

1. Introduction: A Linear Programming Problem

2. What Does Linear Programming Do?

3. Applications of Linear Programming

4. Jarvis & Partners: Developing a Model

5. Summary

Section 2: Developing a Linear Programming Model

1. Introduction

2. Linear Equations and Linear Inequalities

3. More Case Studies

4. Summary

Section 3: Solving Linear Programming Problems Using Graphical Methods

1. Introduction

2. Jarvis Builders Revisited

3. Summary

Section 4: Practising the Graphical Solution Technique

1. Introduction

2. Superb Audio plc: a Graphical Solution

3. The Small Mine: a Graphical Solution

4. Rest Easy Lounge Suites: a Graphical Solution

5. The Doll's Workshop: a Graphical Solution

6. Summary

Section 5: Shadow Prices and Sensitivity Analysis

1.Introduction

2. Scarce Resources and Shadow Prices

3. Calculating Shadow prices

4. Shadow Prices and Sensitivity

5. Summary

Section 6: The Role of Computer Software

1. Introduction

2. The Simplex Algorithm

3. Simplex Linear Programming - Sample Output

4. More Than Two Decision Variables

5. Limitations of Linear Programming

6. Summary

References

Glossary

**UNIT FOUR - REGRESSION AND CORRELATION**

Unit Objectives

Section 1. Relationships Between Variables

1. What is Correlation and Regression?

2. Relationships Between Variables

3. Summary

Section 2. The Coefficient of Correlation

1. Correlation Between Variables

2.The Coefficient of Correlation

3.Interpretation of the Coefficient of Correlation

4. Summary

Section 3. Interpreting the Coefficient of Correlation

1. Linearity

2. Causality

3. Trends

4. Sample Size and Accuracy

5. Non-Ratio Scale Data

6. Summary

Section 4. Regression Analysis

1. What is Regression Analysis

2. The Purpose of Regression

3. Finding the Form of the Regression Equation

4. Best Fit - The Least Squares Method

5. Statistical and Spreadsheet Packages

6. Dependent and Independent Variables

7. Summary

Section 5. How Effective is Regression Analysis?

1. What We Have Accomplished So Far

2. Interpretation of the Coefficient of Determination

3. Summary

Section 6. What Next?

1 Where Do We Go From Here?

2. Correlation, Regression and Non-Ratio Scale Data

3. Dealing With a Time Series

4. What Can We Do About Non-Linearity?

5. Must We Always Be Limited to Two Variables?

6. Summary

References

Glossary

**UNIT FIVE - PROBABILITY**

Unit Objectives

Section 1. The Problem of Measurement

1. Introduction

2. What is Probability

3. Percentages and Odds

4. Summary

Section 2. Events, contingency Tables and Venn

Diagrams

1. Simple and Complex Events

2. Probability Notation and Venn Diagrams

3. Summary

Section 3. Rules for Calculating Probabilities

1. Introduction

2. Conditional Probabilities

3. The Intersection of Events

4. The Union of Events

5. Complementary Events

6. Summary

Section 4. Putting the Rules of Probability to Work

1. Introduction

2. Summary

Section 5. Probability Trees

1. Introduction

2. Probability Trees in Use

3. Summary

Section 6. Counting Techniques

1. Introduction

2. The 'MN' Rule

3. The Permutations Rule

4. The Combinations Rule

5. Summary

References

Glossary

**UNIT SIX - PROBABILITY DISTRIBUTION**

Unit Objectives

Section 1. Random Variables

1. Introduction

2. Discrete and Continuous Variables

3. Probability and Random Variables

4. Probability Distributions

5. What Do Probability Distributions Look Like?

6. Conclusion

7. Summary

Section 2. Mathematical Functions of Probability Distributions

1. Introduction

2. Functions and Discrete Data

3. Functions and Continuous Data

4. Conclusion

5. Summary

Section 3. Summing Up Probability Distributions

1. Introduction

2. Expected Value For a Discrete Variable

3. The Variance of a Discrete Random Variable

4. Expected Value and Variance: Continuous Variables

5. Interpretation of Expected Value and Variance

6. Summary

Section 4. Binomial Distribution

1. Introduction: A Matter of Insurance

2. The General Form of the Binomial Distribution

3. Expected Value and Variance of a Binomial Distribution

4. Summary

Section 5. Normal Distribution

1. Introduction

2. Characteristics of the Normal Distribution

3. Mean and Standard Deviation of the Normal Distribution

4. Probability and Areas Under the Normal Curve

5. The Standard Normal Distribution

6. Summary

Section 6. Using the Normal Distribution

1. Non-Standard Normal Distributions

2. The Normal Curve and Binomial Probabilities

3. Summary

4. Unit Summary and Conclusions

References

Glossary

Tables of Areas Under the Standard Normal Curve

**UNIT SEVEN - INTRODUCTION TO SAMPLING**

Unit Objectives

Section 1 Sample and Population

1. Introduction

2. Random Sampling

3. Selecting a Random Sample

4. Can We Trust Sample Estimates?

5. Summary

Section 2 The Behaviour of Sample Estimates

1. Terminology

2. The Central Limit Theorem

3. Summary

Section 3 Point Estimates and Interval Estimates

1. Problems in Estimation

2. Calculation of Interval Estimates

3. Interpretation of Confidence Intervals

4. How Precise Are Interval Estimates?

5. How Precise Are Sample Estimates?

6. Summary

Section 4 Proportions and Percentages

1. Introduction

2. Sampling Distribution of Proportions

3. Confidence Intervals for Proportions

4. Summary

Section 5 Sample Size Problems

1. Introduction

2. Deciding Sample Size: The Method

3. Proportions and Sample Size Problems

4. Summary

Section 6 Significance Testing

1. Introduction

2. Construction of Statistical Tests

3. Possible Mistakes in Statistical Tests

4. Notes Concerning the Use of Sampling Theory

5. Summary

References

Glossary

Table of Areas Under the Standard Normal Curve

**UNIT EIGHT - INDEX NUMBERS**

Unit Objectives

Section 1 The Measurement of Change

1. Why Measure Change?

2. Simple Index Numbers

3. More Complex Index Numbers

4. The Price Relative Method

5. Summary

Section 2 Weighted Indices and Aggregative Methods of Calculation

1. Weighted Index Numbers

2. Selecting Suitable Weights

3. The Aggregative Method of Calculation

4. Summary

Section 3 Quantity and Value Indices

1. Value and Volume Indices

2. Using a Value Index as a Deflater

3. The UK Retail Prices Index

4. Summary

Section 4 Time Series

1. Introduction

2. A Sales Data Time Series

3. Breaking Down a Time Series

4. Models of Time Series Data

5. Summary

Section 5 Moving Averages

1. Introduction

2. Moving Averages

3. Seasonal Variation

4. Summary

Section 6 Forecasting a Time Series

1. Using Regression Analysis on a Time Series

2. The Multiplicative Model

3. Summary

References

Glossary

## Requirements

There is no experience or previous qualifications required for enrolment on this course. It is available to all students, of all academic backgrounds.

## Assessment

**Assessment Method**

After each lesson there will be a question paper, which needs to be completed and submitted to your personal tutor for marking. This method of continual assessment ensures that your personal tutor can consistently monitor your progress and provide you with assistance throughout the duration of the course.

**What's Included**

- All study materials
- Study Guide
- Full Tutor and Admin support

Need proof of your English and Maths skills? Want to catch up and learn more English and Maths?
You can for free when you sign up to this **learndirect** course.

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