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TP SOLVED SERIES

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RTMNU2018/BCCA-Part-II/TPSS/4/01

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TP SOLVED SERIES
For
BCCA
[Bachelor of Commerce (Computer Application)]
Part-II, Fourth Semester
‘Rashtrasant Tukadoji Maharaj Nagpur University (RTMNU)’
(4T1) MATHEMATICS
 
UNIT-I
Introduction Scope, Data Collection and Classification: Meaning of Statistics, Variable and Attribute, Primary Data and Secondary Data, Population (or Universe) and Sample, Complete Enumeration (or Census) and Sample Survey, Statistical Enquiry, Useful Terms Classification, Tabulation, Mechanical Tabulation. Permutation: Introduction, Fundamental Rules of Counting, Result on Permutation Examples. Combination: Introduction, Result of Combination. Set Theory :Method of Set Representation and Notation, Types of Sets, Venn Diagram, Set Operations, Union(Set Addition), Intersection (Set Multiplication), Complement, Difference, Examples on Set Operations, Laws of Algebra of Sets, Duality, Verification of Laws (Using Venn Diagram), Proof of the Laws of Set Algebra, Number of Elements in a Set.
 
UNIT-II
Logarithm: Introduction, Definition of Logarithm, Laws of Logarithm, Common Logarithm and Natural Logarithm, Antilogarithm. Compound Interest: Interest Compounded Continuously, Amount at the Changing rates of Interest, Nominal and Effective rate of Interest, Growth and Depreciation. Other Useful Mathematics Devices: Rounding of Numbers, Absolute, Relative and Percentage Errors, Significant Figures, Some Short Processes of Calculation, Roots and Reciprocals Expressed as Power, A.P. Series and G.P. Series, Sum and Sum of the Squares of Numbers, Inequalities, Concept of Function, Polynomial, Sigma (Σ) Notation, Simple Interpolation
 
UNIT-III
Charts and Diagrams: Objects of Diagrammatic Representation, Types of Charts and Diagrams. Frequency Distribution: Observation, Frequency, Simple Series(or Ungrouped Data)and Frequency Distribution, Useful Terms Associated with Grouped Frequency Distributions, Construction of frequency Distribution, Cumulative Frequency Distribution, Relative Frequency Distribution, Diagrammatic Representation of Frequency Distributions, Frequency Curve. Measures of Central Tendency :Average or Measure of Central Tendency, Arithmetic Mean(A.M.), Important Properties of A.M., Simplified Calculation for A.M., Mean of Composite Group, Geometric Mean(G.M.), Properties of G.M., Harmonic Mean(H.M.), Advantages and Disadvantages of A.M.,G.M.,H.M., Relations between A.M.,G.M.,H.M., Median, Calculation of Median, Advantage and Disadvantage of Median, Mode, Calculation of Mode, Advantages and Disadvantages of Mode, Relation between Mean, Median, Mode, Partition Values – Quartiles, Deciles, Percentiles, Calculation of Partition Values. Measures of Dispersion: Meaning and Necessity of ‘Measures of Dispersion, Range, Quartile Deviation (Or Semi – Interquartile Range), Mean Deviation (Or Mean Absolute Deviation), Standard Deviation(S.D.), Important Properties of S.D., Calculation of Standard Deviation (σ), S.D. of Composite Group, Relation between S.D. and Other Measures, Relative Measure of Dispersion.
 
UNIT-IV
Moments, Skewness and Kurtosis :Moments, Relation between central and Non-Central moments, Beta coefficients and Gamma-coefficients, Standardized Variable, Moments of Frequency Distributions, Skewness, Kurtosis. Curve Fitting: Curve Fitting, Straight Line and Parabola, Free – hand Method of Curve Fitting, Method of Least squares, Fitting Straight line, Simplified Calculations, Fitting Parabola, Fitting Exponential and Geometric Curves. Correlation and Regression: Concepts of ‘correlation ‘and ‘Regression‘, Bivariate Data, Bivariate, Frequency Distribution, Scatter Diagram, Correlation, Covariance, Correlation Coefficient(r),Properties of Correlation coefficient, Calculation of r, Interpretation and use of r, Variance of the Sum (Difference)of Two Series, Regression, Properties of Linear Regression, Explained Variation and Unexplained Variation, Regression Curve in Bivariate Frequency Distribution , Rank Correlation. Time Series : Meaning and Necessity of ‗Time Series Analysis‘, Components of Time Series, Adjustments to Time Series Data, Secular Trend, Measurement of Trend, Monthly Trend from Annual Data, Seasonal Variation, Measurement of Seasonal Variation, Cyclical Fluctuation, Business Forecasting, Exponential Smoothing. Probability Theory : Introduction, Random Experiment, Outcome, Event, Important Terminology, Techniques of Counting, Classical (or ‘a Priori’)Definition of Probability, Theorems of Probability, Draw without Replacement, Repeated Trials-Drawing with Replacement, Bayes’ Theorem Other Approaches to Probability Theory, Set and Probability, Finite Probability Space and Assignment of Probabilities, Finite Equiprobable Sample Space and Classical Definition, Conditional Probability, Independent Events.


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