1、BUSINESS MATHEMATICS & STATISTICS,BUSINESS MATHEMATICS & STATISTICSLecture 2,COURSE MODULES8 ModulesModules 1-4: MathematicsModules 5-8: Statistics,Module 1Overview (Lecture 1)Applications of Basic Mathematics (Lectures 2-6),LECTURE 2Course OverviewArithmetic Operations&Using Microsoft Excel,ARITHME
2、TIC OPERATIONSAdditionSubtractionMultiplicationDivisionExponent,BUSINESS MATHEMATICS & STATISTICS,BUSINESS MATHEMATICS & STATISTICSLECTURE 3,LECTURE 3EvaluationsCalculate Gross EarningsUsing Microsoft Excel,EvaluationIn order to successfully complete this course, the student is required to meet the
3、evaluation criteria,Evaluation Criterion 1Full participation is expected for this course,Evaluation Criterion 2All assignments must be completed by the closing date,Evaluation Criterion 3Overallgrade will be based on VU existing Grading Rules,Evaluation Criterion 4All requirements must be met in ord
4、er to pass the course,GradingThere will be a term exam and one final exam; there will also be 4 assignments The final exam will be comprehensive,GradingThese will contribute the following percentages to the final grade:Mid Term Exam 35%Final 50%4 Assignments 15%,CollaborationDiscusPrepare own soluti
5、onsMake original submissions,ETHICSNo copyingNo cheatingNo short cuts,MethodologyThere will be 45 lectures each of 50 minutes duration The lectures will be delivered in a mixture of Urdu and English,MethodologyHeavily supported by slide presentationsThe slides available on the VU website before the
6、actual lecture is televised Students to carry out preparatory reading before the lecture,MethodologyOwn page on the VUs web site Lecture and other supporting material Link to a web-based discussion and bulletin board,MethodologyTeaching assistants will be assigned by VU to provide various forms of a
7、ssistance such as grading, answering questions posted by students and preparation of slides,Text and Reference MaterialMaterial from different sources Topics for reading on course web site and in professors handoutsOn the course web site A list of reference books to be posted and updated on course w
8、eb site,PROBLEMSIf you have any problems with understanding of the courseContactbizmathvuedupk,SalaryBasic Salary +Allowances +Gratuity +Provident Fund +Social Charges,AllowancesHouse Rent 45 %Conveyance 2.5 %Utilities 2.5 %,Gratuity1/11 th of Basic Salary About 9.09 % of Basic,Provident Fund1/11 th
9、 of Basic SalaryAbout 9.99 % of Basic,Social Charges Casual Leave 18 DaysSick Leave 12 DaysMedical/Group Insurance 5%Total about 29% of Gross Salary,SummaryBasic salary 100 %Allowances 50 %Gratuity 9.99 %Provident Fund 9.99 %Social Charges 29 %,EXAMPLE 1Basic Salary= 6,000 Rs Calculate Remuneration
10、Including Allowances, Gratuity, Provident Fund and Social Charges,Decimal Fraction = 0.5 10/100=0.1Common Fraction10/100=1/10,PercentFraction X 100Example0.1 X 100= 10%,Converting % into Fraction20%= 20/100= 0.2,Rate Percent or FractionEarnings20% or 20/100=0.2,PercentagePercent of the BaseExample20
11、% of 120In 20% of 120120 is Base20% is Rate,Percentage=Base x Rate20% x 12020/100 x 120Or 0.2 X 120= 24,What Percentage is 6 % of 40= Rate X Base= 0.06 X 40= 24,Base=Percentage/RateExampleRate = 24.0 %Percentage = 96Base= 96/0.24=400,BUSINESS MATHEMATICS & STATISTICS,BUSINESS MATHEMATICS & STATISTIC
12、S,LECTURE 4Review Lecture 3Calculating simple or weighted averagesUsing Microsoft Excel,Lecture 3 ReviewWORKSHEETRemuneration.xls,Average (Arithmetic Mean)=Sum /NSum= Total of numbersN= Number of numbers,EXAMPLE 1 Numbers:10, 7, 9, 27, 2Sum:= 10+7+9+27+2 = 55Numbers = 5Average = 55/5 = 11,ADDING NUM
13、BERS USING MICROSOFT EXCELAdd numbers as you type them Add all numbers in a contiguous row or columnAdd numbers that are not in a contiguous row or columnAdd numbers based on one condition Add numbers based on multiple conditions Add numbers based on criteria stored in a separate rangeAdd numbers ba
14、sed on multiple conditions with the Conditional Sum Wizard,Add numbersAdd numbers as you type themType =5+10 in a cellResult 15.See Example 2,Add all numbers in a contiguous row or column Click a cell below the column of numbers or to the right of the row of numbersClick AutoSum Press ENTER See Exam
15、ple 2,Add numbers that are not in a contiguous row or columnUse the SUM function See Example 3,Add numbers based on one conditionUse the SUMIF function to create a total value for one range, based on a value in another rangeSimilar to Example 4,Add numbers based on multiple conditions Use the IF and
16、 SUM functions to do this task See Example 4,Add numbers based on criteria stored in a separate range Use the DSUM function to do this task Study DSUM Example,DSUMAdds the numbers in a column of a list or database that match conditions you specify.SyntaxDSUM(database,field,criteria)Database is the r
17、ange of cells that makes up the list or database. Field indicates which column is used in the function. Criteria is the range of cells that contains the conditions you specify.,DSUMEXAMPLE=DSUM(A4:E10;Profit“;A1:F2)The total profit from apple trees with a height between 10 and 16 (75),AVERAGE USING
18、MICROSOFT EXCELCalculate the average of numbers in a contiguous row or columnCalculate the average of numbers not in a contiguous row or column,AVERAGEReturns the average (arithmetic mean) of the arguments.SyntaxAVERAGE(number1,number2,.)Number1, number2, . are 1 to 30 numeric arguments for which yo
19、u want the average.,WEIGHTED AVERAGEAv.1 x weight 1 +Av. 2 x weight 2 +.Av. N x weight nWeights in fractions,BUSINESS MATHEMATICS & STATISTICS,BUSINESS MATHEMATICS & STATISTICS,LECTURE 5Review of Lecture 4Basic calculations of percentages, salaries and investments using Microsoft Excel,Mondays Sales
20、 were Rs.1000 and grew to Rs. 2500 the next day Find the percent change,CALCULATIONInitial Value =1000Final Value = 2500 Change = 1500 % Change = 1500/1000 x 100= 150,HOW many Percent is Next Days sale with refernce to Mondays Sale?Mondayss sale= 1000Next days sale= 2500Next days sale as % = 2500/10
21、00 x 100 = 250 %= Two and a half times,reference,ow,ow,reference,In the making of dried fruit, 15kg. of fruit shrinks to 3 kg Find the percent change.,CALCULATIONOriginal fruit = 15 kgFinal fruit = 3 kgChange = 3-15 = -12% change = - 12/15 x 100= - 80 %Size was reduced by 80%,After mixing with water
22、 the weight of cotton increased from 3 kg to 15 kg Find the percent change.,CALCULATIONOriginal weight = 3 kgFinal weight = 15 kgChange = 15-3= 12% change = 12/3 x 100= 400 %Weight increased by 400%,A union signed a three year collective agreement that provided for wage increases of 3%, 2%, and 1% i
23、n successive yearsAn employee is currently earning 5000 rupees per month What will be the salary per month at the end of the of the term of the contract?,CALCULATION5000(1 + 3%)(1 + 2%)(1 + 1%)=5000 x 1.03 x 1.02 x 1.01,Investment for a period of 4 years Rates of return for each year are 4%, 8%, -10
24、% and 9% respectively. If you invested Rs. 100,000 at the beginning of the term, how much will you have at the end of the last year?,BUSINESS MATHEMATICS & STATISTICS,BUSINESS MATHEMATICS & STATISTICS,LECTURE 6Review Lecture 5DiscountSimple and compound interest Average due date, interest on drawing
25、s and calendar,Revision Lecture 5A chartered bank is lowering the interest rate on its loans from 9% to 7%.What will be the percent decrease in the interest rate on a given balance?,A chartered bank is increasing the interest rate on its loans from 7% to 9%What will be the percent increase in the in
26、terest rate on a given balance?,Investors,Stock Quotation Calculations,Closing price per share,Annual dividend per share,=,10,41.125,=,.3%,Closing price per share,Annual earnings per share,=,41.125,1.11,Total # of shares outstanding,Annual earnings,=,100,000,1,000,000,= $0.10,BUYING SHARESIf you buy
27、 100 shares at Rs. 62.50 per share with a 2% commission, calculate your total cost,CALCULATION100 * Rs. 62.50 = Rs. 6,250.02 * Rs. 6,250 = 125 Rs. 6,375,RETURN ON INVESTMENTSuppose you bought 100 shares at Rs. 52.25 and sold them 1 year later at Rs. 68. With a 1% commission rate buying and selling t
28、he stock and a current Rs 10 dividend per share in effect, what was your return on investment?,Bought100 shares at Rs. 52.25 = 5,225.00Commission at 1% = 52.25Total Costs = 5,277.25,Sold100 shares at Rs. 68 = 6,800.00Commission at 1% = - 68.00Total Costs = 6,732.00,GainNet receipts = 6,732.00Total c
29、ost =- 5,277.25Net Gain = 1,454.75Dividends (100*1) = 100.00Total Gain = 1,554.75Return on investment = 1,554.75/ 5277.25*100 = 29.46 %,DiscountRebate or reduction in priceExpressed as %,DiscountList price = 2200Discount Rate = 155Discount?= 2200 x 0.15= 330,Net Cost Price= List price - DiscountList
30、 price = 4,500 Rs.Discount = 20 %Net cost price = 4,500 20 % of 4,500= 4,500 0.2 x4,500=4,500 900= 3,600 Rs.,Simple InterestI = P. R. T / 100P = PrincipalR = Rate percent per annumT = Time in yearsI = Simple interest,Find interestP = Rs. 500T = 4 yearsR =11% I = P x T x R /100= 500 x 4 x 11/100= Rs.
31、 220,Compound InterestAlso attracts interestP = 800Interest year 1= 0.1 x 800= 80New P = 800 + 80 = 880Interest on 880 = 0.1 X 880 = 88New P = 880 + 88 = 968,Compound Interest FormulaS= Money accrued after n yearsP= PrincipalR= RateN= Number of yearsS = P(1 + r/100) n,ExampleCalculate interest on Rs
32、. 750 invested at 12% per annum for 8 years.S= P(1+r/100)8= 750(1+12/100)8= 1957,BUSINESS MATHEMATICS & STATISTICS,BUSINESS MATHEMATICS & STATISTICS,Module 2Exponents and RadicalsLinear Equations (Lectures 7)Investments (Lectures 8)Matrices (Lecture 9)Ratios & Proportions and Index Numbers (Lecture
33、10),LECTURE 7Review of lecture 6Exponents and radicals Simplify algebraic expressions Solve linear equations in one variable Rearrange formulas to solve for any of its contained variables,AnnuityValue = 4,000Down payment = 1,000Rest in 20 installments of 200Sequence of payments at equal interval of
34、timeTime = Payment Interval,NOTATIONSR = Amount of annuityN = Number of paymentsI = Interest rater per conversion periodS = Accumulated valueA = Discounted or present worth of an annuity,ACCUMULATED VALUES = r (1+i)n 1)/iA = r (1- 1/(1+i)n)/i)Accumulated value= Payment x Accumulation factorDiscounte
35、d value= Payment x Discount factor,ACCUMULATION FACTOR (AF)i = 4.25 %n = 18AF = (1 + 0.0425)18-1)= 26.24R = 10,000Accumulated value = 10,000x 26.24= 260,240,DISCOUNTED VALUEValue of all payments at the beginning of term of annuity= Payment x Discount Factor (DF) DF = (1-1/(1+i)n)/i)= (1-1/(1+0.045)8
36、)/0.045)= 6.595,ACCUMULATED VALUE= 2,000 x (1-1/(1+0.055)8)/0.055)= 2,000 x11.95=23,900.77,Algebraic Expression,indicates the mathematical operations to be carried out on a combination of NUMBERS and VARIABLES,Terms,the components of an Algebraic Expression that are separated by ADDITION or SUBTRACT
37、ION signs,x(2x2 3x 1),Terms,1 Term,2 Terms,3 Terms,any more than 1 Term!,3x2,3x2 + xy,3x2 + xy 6y2,Term,each one in an Expression consists of one or more FACTORS separated by MULTIPLICATION or DIVISION sign,xy = x*y,Also,assumed when one factor is written under an other!,Term,Numerical Coefficient,L
38、iteral Coefficient,FACTOR,3x2,Algebraic Expression,Terms,Division by a Monomial,Identify Factors in the numerator and denominator,36x2y,3(12)(x)(x)(y),60xy2,5(12)(x)(y)(y),Cancel Factors in the numerator and denominator,=,Division by a Monomial,Divide each TERM in the numerator by the denominator,Ca
39、ncel Factors in the numerator and denominator,48a2/8a 32ab/8a or,6,4,=,48(a)(a),32ab,-,8a,8a,= 6a, 4b,Multiplying Polynomials,Multiply each term in the TRINOMIAL by (x),+,+,=,=,-2x3,+,3x2,+,The product of two negative quantities is positive.,x,Exponents Rule of,= 32*4,34,Base,3,Exponent,4,3,i.e. 3*3
40、*3*3,Power,= 81,32 *33,= 32 + 3,= 3,5,= 243,(32)4,=(1+ i)20-8,= (1+ i),12,= 3,8,= 6561,Exponents Rule of,X4,=,Z3*2,z6,Solving Linear Equations in one Unknown,Equality in Equations,A + 9,Expressed as: A + 9 = 137 A = 137 9 A = 128,Solving Linear Equations in one Unknown,Solve for x from the following
41、: x = 341.25 + 0.025x,x - 0.025x = 341.25,0.975x = 341.25,x = 341.25 + 0.025x,x = 341.25 0.975,x = 350,BUSINESS MATHEMATICS & STATISTICS,Solving Word Problems,for the Unknown,Barbie and Ken sell cars at the Auto World.,Data,In April they sold 15 cars.,Barbie sold twice as many cars as Ken.,How many
42、cars did each sell?,2C + C = 15 3C = 15,C = 5,Barbie = 2 C = 10 Cars,Ken = C = 5 Cars,Barbie sold twice as many cars as Ken.,In April they sold 15 cars.,Colleen, Heather and Marks partnership interests in Creative Crafts are in the ratio of their capital contributions of $7800, $5200 and $6500 respe
43、ctively.,What is the ratio of Colleens to Heathers to Markss partnership interest?,Colleen, Heather and Marks partnership interests in Creative Crafts are in the ratio of their capital contributions of $7800, $5200 and $6500 respectively.,7800,5200,:,6500,:,Colleen,Heather,Mark,Equivalent ratio (eac
44、h term divided by 100),78,52,65,:,:,Equivalent ratio with lowest terms,1.5 : 1 : 1.25,The ratio of the sales of Product X to the sales of Product Y is 4:3. The sales of product X in the next month are forecast to be $1800.,What will be the sales of product Y if the sales of the two products maintain the same ratio?,Expressinga Ratio inEquivalent Forms,A 560 bed hospital operates with 232 registered nurses and 185 other support staff. The hospital is about to open a new 86-bed wing.,
