Course title: Business Mathematics and StatisticsB.Com (Term System) Term-I Paper-V
Course objectives:
Upon completion of this course, students are expected to be able to:
1.Develop an understanding of the selected Mathematical and Statistical concepts as well as their application in the situations encountered in business and commerce.
2.Develop competency in fundamental arithmetic through practical applications.
3.Get background of Statistical Methods required for other courses in business, economics and commerce.
4.Obtain basic skills in using Statistical Computer Packages to assist in performing necessary computations required in a statistical analysis through practical applications.
Course contents/ Lesson Plan
Topic / Books to be consulted / SectionSimultaneous equation system. / A
Introduction to the System of Simultaneous Equations and its Practical Applications.
- Solution of the System of Simultaneous Equations
- Introduction to Quadratic Equations and Quadratic Formula
Chapter1
Sequence, Series and Progression / A
- Sequence, Series and Progression: Introduction and Comparison thereof
- Arithmetic Series and its application in business
- Geometric Series and its application in business
Chapter1
Matrix Algebra / A
- Introduction to Matrices
- Type of Matrices (Symmetric, Identity, Square)
- Use of Matrices
- Addition
- Subtraction
- Multiplication
- Determinant, Adjoint and Inverse of matrix
- Solution of linear equations through matrices
Chapters 3 & 9
Differentiation / A
Introduction to Differential calculus and differentiation of functions
Partial Differentiation, First and Second Derivatives
- Application of derivatives in Business and Commerce
- Optimization
Chapters 13&14
Mathematics of Finance / A
Interest and its computation
Annuities and their future value
Annuities and their present value
Application of interest in Business and Commerce / Book 2
Chapter 8
Introduction of Statistics / A
- Definition and meaning of Statistics
- Type of Statistics
- Application in Business and Commerce
Chapters 1 & 2
Data Summarization
- Data collection
- Source of statistical data
- Application of Computer in summarizing data
- Frequency Distribution
- Graphical representation of data (manual and computer based)
Measure of Central Tendency / A
Idea of Average and Types of Averages
- Median: Need and uses
- The Mode: Need and Uses
Geometric Mean and its application
Computer Based calculation of Averages / Book 3
Chapter 3
Measure of Dispersion / B
Definition of Dispersion
- The Range
- The Quartile Deviation
- The Mean Deviation
Chapter 3
- Properties of Variance and Standard Deviation
- Coefficient of Variation : Need and Uses
- Symmetric and Non-symmetric distributions
- Computer based calculation of Dispersion
Basic Probability Theory / B
Prerequisites
Random Experiment
Events and its type
- Definitions of Probability
Addition and Multiplication laws of Probability
Independent and Dependent Events.
Application of Probability Theory in Business / Book 3
Chapters 4 & 5
Random variable and Probability Distribution / B
Introduction to Random Variable and its type
Probability Distributions and their types
Type of Probability Distribution
Discrete Probability Distribution
Continuous Probability Distribution
Distribution Functions
Expected values of random variable, Variance of random variables / Book 3
Chapters 6 & 7
Binomial Distribution
Basic properties and application
Hypergeometric distribution
Basic properties and application
Normal Distribution
Basic properties an application
Normal approximation to the Binomial, Continuity correction factor / Book 1
Chapters 8 & 9 / B
Recommended Texts:
- Bowen, E.K., and Starr, M.K. (1982), “Basic Statistics for Business and Economics”, McGraw-Hill Education
- Budnick, F.S. (1993), “Applied Mathematics for Business, Economics and Social Sciences”, 4th Edition, McGraw Hill.
- Webster, A.L. (1997), “Applied Statistics for Business and Economics” 3rd Edition.
Further Readings
- Anderson, D.R., Sweeney, D.J., and Williams, T.A., (2007) “Statistics for Business and Economics”,10thEditionSouth-WesternCollege Publications
- McClave, J. and Benson, P.G.(1991), “Statistics for Business and Economics”, Maxwell Macmillan International.
- Stanley J., Farlow, G. and Haggard, M (1988), “Applied Mathematics for Management, Life Sciences and Social Sciences:,
- Swift, L., (1997), “Mathematics and Statistics for Business, Management and Finance”, Maxwell Macmillan international.
MODEL PAPER FOR B.COM Term-I
BUSINESS MATHEMATICS AND STATISTICS
SECTION II & III
Time Allowed = 100 minutes (1hour and 40 Minutes)
Section II SAQs- (Attempt all questions)No. of Questions =11
Marks=22
Q. 1) Answer Following Short Questions. (11 × 2 = 22 Marks)
a)Why System of Simultaneous Equations is called “Simultaneous”?
b)What is meant by solution of a Quadratic Equation?
c)Differentiate Sequence, Series and Progression.
d)What are the conditions which make the matrices A and B conformable for multiplication as AB?
e)What are the conditions for the matrix A so as A-1 could be calculated?
f)What are the situations when first derivative equals Zero?
g)What are the important sources of statistical data?
h)Discuss the empirical relation between Mean, Median, and Mode.
i)Compare Relative and Absolute dispersion.
j)Compare Subjective and Objective Probability.
k)Importance of Probability Distributions in Business.
SECTION-III (Essay Type Questions) Marks=30
Note: Attempt ONE question from each Part.
PART-A
Q. 2)(5 + (5 + 5) = 15 Marks)
The solution to a system of equation having the form AX = B can be found by matrix multiplication.
a)What was the original system of equation?
b)Solve the system of equation by
i)Elimination Method
ii)Matrix manipulation
Q. 3)(4+ 4 + 7 = 15 Marks)
a)Differentiate the following with respect to x
i)
ii)
b)Complete the table and then calculate mean and median
6-8 / - / - / -
8-10 / 23 / - / 29
10-12 / - / 0.34 / -
12-14 / 17 / 0.17 / -
14-16 / - / - / 92
16-18 / - / - / -
Total / 100
PART-B
Q. 4)(5 + (3 + 4 + 4) = 15 Marks)
a)What is meant by skewed distributions? Depict it. Can it be assessed by means of mean, median, and mode? How?
b)Construct a probability distribution based on the following frequency distribution.
Frequency / 10 / 20 / 45 / 15 / 20 / 15
i)Draw a graph of the hypothetical probability distribution
ii)Compute the expected value of the outcome
Q. 5)(5 + (3 + 4 + 4) = 15 Marks)
a)How computer can assist in applying statistical techniques to business concerns?
b)A batch of 5000 electric lamps has a mean life of 1000 hours and a standard deviation of 75 hours. Assume a normal distribution.
i)How many lamps will fail before 900 hours?
ii)What percentage of lamps will fail before 925 hours?
iii)What is the life in hours for the most durable 3% electric bulbs?
MODEL PAPER FOR B.COM Term-I
BUSINESS MATHEMATICS AND STATISTICS
SECTION-I(MCQs- All questions are to be attempted) Time Allowed = 23 Minutes
No. of Questions =23
Marks=23
INSTRUCTIONS TO CANDIDATES:
- Encircle the correct option only.
- Cutting, overwriting and use of ink remover is not allowed.
Q 1)Which of the following can be used to construct frequency distribution?
a)Minitab
b)MS Excel
c)Both (a) and (b) above
d)Neither (a) nor (b)
Q 2)What is true about median?
a)It does not get affected by the extreme values
b)It is equal to the second quartile
c)Both (a) and (b) above
d)Neither (a) nor (b) above
Q 3)Which of the following is relative measure of dispersion?
a)Variance
b)Standard Deviation
c)Coefficient of Variation
d)None of the above
Q 4)Probability can be considered as:
a)The quantification of uncertainty
b)The qualification of uncertainty
c)Both of the above
d)None of the above
Q 5)Probability can only take values ranging:
a)From 0, i.e. certainty, to 1, i.e. impossibility
b)From 0, i.e. uncertainty, to 1, i.e. certainty
c)From 0, i.e. impossibility, to 1, i.e. certainty
d)None of the above
Q 6)Where the probability of an event is based on past data and the circumstances are repeatable by test, the probability is known as
a)Relative Probability
b)Absolute Probability
c)Subjective probability.
d)Objective Probability
Q 7)Mutually exclusive events are the events which:
a)Can happen at the same time
b)Cannot happen at the same time
c)Do happen at the same time
d)Are necessarily independent to each other
Q 8)For mutually exclusive events X and Y
P(X OR Y) =
a)P(X) ÷ P(Y)
b)P(X) - P(Y)
c)P(X) × P(Y)
d)P(X) + P(Y)
Q 9)A histogram is a set of vertical bars or columns:
a)Whose areas are not proportional to the frequencies represented.
b)Whose areas are proportional to the frequencies represented.
c)Whose heights (not areas) are proportional to the frequencies represented.
d)Whose areas are independent to the frequencies represented.
Q 10)In a symmetrical distribution:
a)The mean, median and harmonic mean have the same value.
b)The mean, median and Standard Deviation have the same value.
c)The mean, median and Mode have the same value.
d)The mean, Variance and Standard Deviation have the same value.
Q 11)What is true for equations?
a)Real-valued expressions which are equal can be added to both sides of an equation
b)Real-valued expressions which are equal can be subtracted from both sides of an equation
c)Both (a) and (b) above
d)Neither (a) nor (b) above
Q 12)How many roots of a quadratic equation are there?
a)Four
b)Three
c)Up to two
d)None of the above
Q 13)If a matrix has three rows and four columns its order will be:
a)3 × 4
b)4 × 3
c)3 × 3
d)4 × 4
Q 14)Two matrices and are said to be conformable for multiplication as AB:
a)If
b)If
c)
d)
Q 15)The optimization refers to the study of problems in which one seeks to:
a)Minimize a real function by systematically choosing the values of real or integer variables from within an allowed set.
b)Maximize a real function by systematically choosing the values of real or integer variables from within an allowed set.
c)(a) OR (b) above
d)None of the above
NOTE: Only 15 MCQs are provided for specimen purposes. Actual paper will comprise 23 MCQs (About half of the MCQs from each section of syllabus)