Table Of Content

Business Mathematics & Statistics (MTH 302) Business Mathematics & Statistics (MTH 302) VU TABLE OF CONTENTS : Lesson 1 :COURSE OVERVIEW.......................................................................................................3 Lesson 2 :APPLICATION OF BASIC MATHEMATICS....................................................................12 Lesson 3 :APPLICATION OF BASIC MATHEMATICS....................................................................22 Lesson 4 :APPLICATION OF BASIC MATHEMATICS....................................................................29 Lesson 5 :APPLICATION OF BASIC MATHEMATICS..................................................................399 Lesson 6 :APPLICATION OF BASIC MATHEMATICS....................Error! Bookmark not defined.8 Lesson 7 :APPLICATION OF BASIC MATHEMATICS....................Error! Bookmark not defined.9 Lesson 8 :COMPOUND INTEREST...............................................................................................709 Lesson 9 :COMPOUND INTEREST...............................................................................................776 Lesson 10:MATRICES....................................................................................................................809 Lesson 11: MATRICES...................................................................................................................854 Lesson 12 :RATIO AND PROPORTION..........................................................................................94 Lesson 13 :MATHEMATICS OF MERCHANDISING...................................................................1009 Lesson 14 :MATHEMATICS OF MERCHANDISING.....................................................................105 Lesson 15 :MATHEMATICS OF MERCHANDISING.................................................................11211 Lesson 16 :MATHEMATICS OF MERCHANDISING.................................................................12120 Lesson 17 :MATHEMATICS FINANCIAL MATHEMATICS........................................................12524 Lesson 18 :MATHEMATICS FINANCIAL MATHEMATICS........................................................13029 Lesson 19 :PERFORM BREAK-EVEN ANALYSIS....................................................................13433 Lesson 20 :PERFORM BREAK-EVEN ANALYSIS....................................................................14241 Lesson 21 :PERFORM LINEAR COST-VOLUME PROFIT AND BREAK-EVEN ANALYSIS....14746 Lesson 22 :PERFORM LINEAR COST-VOLUME PROFIT AND BREAK-EVEN ANALYSIS....15049 Lesson 23 :STATISTICAL DATA REPRESENTATION................................................................1587 Lesson 24 :STATISTICAL REPRESENTATION........................................................................16362 Lesson 25 :STATISTICAL REPRESENTATION........................................................................17170 Lesson 26 :STATISTICAL REPRESENTATION........................................................................18079 Lesson 27 :STATISTICAL REPRESENTATION........................................................................18988 Lesson 28 :MEASURES OF DISPERSION................................................................................20099 Lesson 29 :MEASURES OF DISPERSION....................................................................................207 Lesson 30 :MEASURE OF DISPERASION....................................................................................217 Lesson 31 :LINE FITTING..........................................................................................................22524 Lesson 32 :TIME SERIES AND..................................................................................................24039 Lesson 33 :TIME SERIES AND EXPONENTIAL SMOOTHING................................................25352 Lesson 34 :FACTORIALS...........................................................................................................26059 Lesson 35 :COMBINATIONS.........................................................................................................269 Lesson 36 :ELEMENTARY PROBABILITY................................................................................27675 Lesson 37:PATTERNS OF PROBABILITY: BINOMIAL, POISSON AND NORMAL DISTRIBUTIONS .................................................................................................................................27978 Lesson 38:PATTERNS OF PROBABILITY: BINOMIAL, POISSON AND NORMAL DISTRIBUTIONS .................................................................................................................................28483 Lesson 39:PATTERNS OF PROBABILITY: BINOMIAL, POISSON AND NORMAL DISTRIBUTIONS .................................................................................................................................29796 Lesson 40:PATTERNS OF PROBABILITY: BINOMIAL, POISSON AND NORMAL DISTRIBUTIONS .....................................................................................................................................302 Lesson 41: ESTIMATING FROM SAMPLES: INFERENCE..........................................................314 Lesson 42 :ESTIMATING FROM SAMPLE : INFERENCE............................................................320 Lesson 43 :HYPOTHESIS TESTING: CHI-SQUARE DISTRIBUTION..........................................325 Lesson 44 :HYPOTHESIS TESTING : CHI-SQUARE DISTRIBUTION.........................................328 Lesson 45 :PLANNING PRODUCTION LEVELS: LINEAR PROGRAMMING...............................335 2 © Copyright Virtual University of Pakistan Business Mathematics & Statistics (MTH 302) VU MTH 302 LECTURE 1 COURSE OVERVIEW COURSE TITLE The title of this course is “BUSINESS MATHEMATICS AND STATISTICS”. Instructor’s Resume The instructor of the course is Dr. Zahir Fikri who holds a Ph.D. in Electric Power Systems Engineering from the Royal Institute of Technology, Stockholm, Sweden. The title of Dr. Fikri’s thesis was “Statistical Load Forecasting for Distribution Network Planning”. Objective The purpose of the course is to provide the student with a mathematical basis for personal and business financial decisions through eight instructional modules. The course stresses business applications using arithmetic, algebra, and ratio-proportion and graphing. Applications include payroll, cost-volume-profit analysis and merchandising mathematics. The course also includes Statistical Representation of Data, Correlation, Time Series and Exponential Smoothing, Elementary Probability and Probability Distributions. This course stresses logical reasoning and problem solving skills. Access to Microsoft Excel software is required for the course. Course Outcomes Successful completion of this course will enable the student to: 1. Apply arithmetic and algebraic skills to everyday business problems. 2. Use ratio, proportion and percent in the solution of business problems. 3. Solve business problems involving commercial discount, markup and markdown. 4. Solve systems of linear equations graphically and algebraically and apply to cost volume- profit analysis. 5. Apply Statistical Representation of Data, Correlation, Time Series and Exponential Smoothing methods in business decision making 6. Use elementary probability theory and knowledge about probability distributions in developing profitable business strategies. Unit Outcomes Resources/Tests/Assignments Successful completion of the following units will enable the student to apply mathematical methods to business problems solving. Required Student Resources (Including textbooks and workbooks) Text: Selected books on Business Mathematics and Statistics. Optional Resources Handouts supplied by the professor. Instructor’s Slides Online or CD based learning materials. Prerequisites The students are not required to have any mathematical skills. Basic knowledge of Microsoft Excel will be an advantage but not a requirement. Evaluation In order to successfully complete this course, the student is required to meet the following evaluation criteria: Full participation is expected for this course All assignments must be completed by the closing date. Overall grade will be based on VU existing Grading Rules. All requirements must be met in order to pass the course. 3 © Copyright Virtual University of Pakistan Business Mathematics & Statistics (MTH 302) VU COURSE MODULES The following are the main modules of this course: Module 1 • Overview (Lecture 1) • Perform arithmetic operations in their proper order (Lecture 2) • Convert fractions their percent and decimal equivalents. (Lecture 2) • Solve for any one of percent, portion or base, given the other two quantities. (Lecture 2) • Using Microsoft Excel (Lecture 2) Calculate the gross earnings of employees paid a salary, an hourly wage or commissions. (Lecture 3) • Calculate the simple average or weighted average given a set of values. (Lecture 4) Perform basic calculations of the percentages, averages, commission, brokerage and discount (Lecture 5) • Simple and compound interest (Lecture 6) • Average due date, interest on drawings and calendar (Lecture 6) Module 2 • Exponents and radicals (Lecture 7) • Solve linear equations in one variable (Lecture 7) • Rearrange formulas to solve for any of its contained variables (Lecture 7) • Solve problems involving a series of compounding percent changes (Lecture 8) • Calculate returns from investments (Lecture 8) • Calculate a single percent change equivalent to a series of percent changes (Lecture 8) • Matrices ( Lecture 9) • Ratios and Proportions ( Lecture10) • Set up and manipulate ratios ( Lecture11) • Allocate an amount on a prorata basis using proportions ( Lecture11) • Assignment Module 1-2 Module 3 • Discounts ( Lectures 12) • Mathematics of Merchandising ( Lectures 13-16) Module 4 • Applications of Linear Equations ( Lecture 17-18) • Break-even Analysis ( Lecture 19-22) • Assignment Module 3-4 • Mid-Term Examination Module 5 • Statistical data ( Lectures 23) • Measures of central tendency ( Lectures 24-25) • Measures of dispersion and skewness ( Lectures 26-27) Module 6 • Correlation ( Lectures 28-29) • Line Fitting (Lectures 30-31) • Time Series and Exponential Smoothing ( Lectures 31-33) • Assignment Module 5-6 Module 7 • Factorials ( Lecture 34) • Permutations and Combinations ( Lecture 34) • Elementary Probability ( Lectures 35-36) • Patterns of probability: Binomial, Poisson and Normal Distributions ( Lecture 37-40) Module 8 • Estimating from Samples: Inference ( Lectures 41-42) • Hypothesis testing : Chi-Square Distribution ( Lectures 43-44) • Planning Production Levels: Linear Programming (Lecture 45) 4 © Copyright Virtual University of Pakistan Business Mathematics & Statistics (MTH 302) VU • Assignment Module 7-8 • End-Term Examination Note: The course modules are subject to change. MARKING SCHEME As per VU Rules DESCRIPTION OF TOPICS LECTURE RECOMMENDED NO. MAIN TOPIC TOPICS READING 1 1.0 Module Applications of • Overviewew (Lecture 1) Reference 1 1 Basic Mathematics ( Lectures 1-6) 2 Reference 2, • Course Overview Module Lecture 2 • Arithmetic Operations & 1 Tool: Microsoft • Using Microsoft Excel Excel 3 Reference 2, Module • Calculate Gross Earnings Lecture 3 1 • Using Microsoft Excel Tool: Microsoft Excel 4 Reference 2, • Calculating simple or Lecture 4 Module weighted averages Tool: Microsoft 1 • Using Microsoft Excel Excel Reference 6 5 Reference 2, • Basic calculations of Lecture 5 percentages, averages, commission, Module Reference 3, Ch 3 brokerage and discount using 1 Tool: Microsoft • Microsoft Excel Excel 6 Reference 2, • Simple and compound Lecture 6 Module interest Reference 3, Ch 3 1 • Average due date, interest on drawings and calendar Tool: Microsoft Excel 7 • Exponents and radicals Reference 2, • Simplify algebraic 2.0 Lecture 7 expressions Module Applications of Reference 3, Ch 2 • Solve linear equations in one 2 Basic Algebra Tool: Microsoft variable ( Lectures 7-9) Excel • Rearrange formulas to solve for any of its contained variables 5 © Copyright Virtual University of Pakistan Business Mathematics & Statistics (MTH 302) VU 8 • Calculate returns from investments Reference 2, • Problems involving a series Lecture 8 of Reference 3, Ch 3 compounding percent changes • Single percent change Tool: Microsoft equivalent Excel to a series of percent changes 9 Reference 2, Lecture 9 Reference 3, Ch 4 • Matrices Tool: Microsoft Excel 10 • Set up and manipulate ratios. Reference 2, 3.0 • Set up and solve proportions. Lecture 10 Applications • Express percent differences Reference 3, Ch 3 Module of Ratio and using proportions. 2 Proportion • Allocate an amount on a ( Lectures 10- prorata basis using Tool: Microsoft 11) proportions. Excel 11 Reference 2, Lecture 11 • Set up and manipulate ratios. Module Reference 3, Ch 3 • Allocate an amount on a 2 Tool: Microsoft prorata basis using proportions Excel 12 4.0 • Calculate the net price of an Reference 2, Merchandising item after single or multiple trade Lecture 12 Module and Financial discounts. Reference 3, Ch 3 3 Mathematics • Calculate an equivalent single ( Lectures 12- discount rate given a series of Tool: Microsoft 16) discounts. Excel 13 Reference 2, Lecture 13 • Solve merchandising pricing Module Reference 3, Ch 3 problems involving markup and 3 Tool: Microsoft markdown. Excel 14 Reference 2, Lecture 14 Reference 3, Ch 3 Module • Financial Mathematics Part 1 Reference 5, Ch 16 3 Tool: Microsoft Excel Module 15 • Financial Mathematics Part 2 Reference 2, 3 Lecture 15 6 © Copyright Virtual University of Pakistan Business Mathematics & Statistics (MTH 302) VU Reference 3, Ch 3 Reference 5, Ch 16 Tool: Microsoft Excel 16 Reference 2, Lecture 16 Reference 3, Ch 3 Module • Financial Mathematics Part 3 Reference 5, Ch 16 3 Tool: Microsoft Excel 17 Reference 2, Lecture 17 5.0 Break-Even Reference 3, Ch 3 Module Analysis • Graph a linear equation in two Reference 5, Ch 16 4 ( Lectures 17- variables. & 18 22) Tool: Microsoft Excel 18 Reference 2, Lecture 18 • Solve two linear equations Reference 3, Ch 2 Module with two unknowns Reference 5, Ch 1 4 Tool: Microsoft Excel 19 • Perform linear cost-volume Reference 2, Module profit and break-even analysis. Lecture 19 4 • Using a break-even chart Tool: Microsoft Excel 20 • Perform linear cost-volume profit and break-even analysis. Reference 2, Module • Using the algebraic approach Lecture 20 4 of solving the cost and revenue Tool: Microsoft functions Excel 21 • Perform linear cost-volume Reference 2, profit and break-even analysis. Module Lecture 21 • Using the contribution margin 4 Tool: Microsoft approach Excel 22 • Perform linear cost-volume Reference 2, profit and break-even analysis. Module Lecture 22 • Using Microsoft Excel 4 Tool: Microsoft • Assignment Module 3-4 Excel • Mid-Term Examination 6. Statistical 23 Reference 2, Module Representation • Statistical Data Lecture 23 5 of Data Reference 5, Ch 5 ( Lectures 23- Tool: Microsoft 7 © Copyright Virtual University of Pakistan Business Mathematics & Statistics (MTH 302) VU 27) Excel 24 Reference 2, Lecture 24 • Statistical Representation Module Reference 4, Ch 3 Measures of Central Tendency 5 Reference 5, Ch 6 Part 1 Tool: Microsoft Excel 25 Reference 2, • Statistical Representation Lecture 25 • Measures of Central Module Reference 4, Ch 3 Tendency 5 Reference 5, Ch 6 Part 2 Tool: Microsoft Excel 26 Reference 2, Lecture 26 • Measures of Dispersion and Module Reference 4, Ch 4 Skewness 5 Reference 5, Ch 6 Part 1 Tool: Microsoft Excel 27 Reference 2, Lecture 27 Reference 4, Ch 4 • Measures of Dispersion and Reference 5, Ch 6 Module Skewness Tool: Microsoft 5 Part 2 Excel 7. Correlation, 28 Reference 2, Time Series Lecture 28 and Reference 5, Ch Module Exponential • Correlation 13 6 Smoothing Part 1 ( Lectures 28- Tool: Microsoft 33) Excel 29 Reference 2, Lecture 29 Reference 5, Ch • Correlation 13 Part 2 Tool: Microsoft Excel 30 Reference 2, Lecture 30 Reference 5, Ch • Line Fitting 14 Part 1 Tool: Microsoft Excel 8 © Copyright Virtual University of Pakistan Business Mathematics & Statistics (MTH 302) VU 31 Reference 2, • Line Fitting Lecture 31 Part 2 Tool: Microsoft Excel 32 Reference 2, Lecture 32 Reference 5, Ch • Time Series and 15 • Exponential Smoothing Tool: Microsoft Part 1 Excel 33 Reference 2, Lecture 33 • Time Series and Reference 5, Ch • Exponential Smoothing 15 Part 2 • Assignment Module 5-6 Tool: Microsoft Excel 34 Reference 2, 7. Elementary Lecture 34 Probability • Factorials Reference 3, Ch 2 Module ( Lectures 34- • Permutations and 7 38) Combinations Tool: Microsoft Excel 35 Reference 2, Lecture 35 • Elementary Probability Reference 5, Ch 8 Module Part 1 7 Tool: Microsoft Excel 36 Reference 2, Lecture 36 • Elementary Probability Reference 5, Ch 8 Module Part 2 Tool: Microsoft 7 Excel 37 Reference 2, • Patterns of probability: Lecture 39 Binomial, Poisson and Normal Module Reference 5, Ch 9 Distributions 7 Part 1 Tool: Microsoft Excel 38 Reference 2, • Patterns of probability: Lecture 40 Module Binomial, Poisson and Normal Reference 5, Ch 9 7 Distributions Tool: Microsoft Part 2 Excel 9 © Copyright Virtual University of Pakistan Business Mathematics & Statistics (MTH 302) VU 39 Reference 2, • Patterns of probability: Lecture 41 Module Binomial, Poisson and Normal Reference 5, Ch 9 7 Distributions Part 3 Tool: Microsoft Excel 40 Reference 2, • Patterns of probability: Lecture 41 Module Binomial, Poisson and Normal Reference 5, Ch 9 7 Distributions Part 4 Tool: Microsoft Excel 8. Probability 41 Reference 2, Distributions Lecture 42 ( Lectures 39- • Estimating from Samples: Reference 5, Ch Module 44) Inference 10 8 9. Linear Part 1 Programming Tool: Microsoft (Lecture 45) Excel 42 Reference 2, Lecture 43 • Estimating from Samples: Reference 5, Ch Module Inference 10 8 Part 2 Tool: Microsoft Excel 43 Reference 2, Lecture 44 Module • Hypothesis testing : Chi- Reference 5, Ch 11 8 Square Distribution Part 1 Tool: Microsoft Excel 44 Reference 2, Lecture 45 • Hypothesis testing : Chi- Module Reference 5, Ch Square Distribution Part 2 8 11 Tool: Microsoft Excel 45 Reference 2, • Production Planning: Lecture 45 Linear Programming Module Reference 5, Ch • Assignment Module 7-8 8 18 • End Term Examination Tool: Microsoft Excel Methodology There will be 45 lectures each of 50 minutes duration as indicated above. The lectures will be delivered in a mixture of Urdu and English. The lectures will be heavily supported by slide presentations. The slides for a lecture will be made available on the VU website for the course a few days before the actual lecture is televised. This will allow students to carry out preparatory reading before the lecture. The course will be provided its own page on the VU’s web site. This will be used to 10 © Copyright Virtual University of Pakistan