Statistics – PUC 1st Year Karnataka

  • Unit I : Introduction to Statistics and some basic concepts.
    • Meaning – Origin – Scope. Definitions –singular and plural sense. Characteristics, Branches, Functions and limitations. Statistical applications in other subjects. Distrust of Statistics – causes and remedies. Some basic concepts – units, population, sample, qualitative characteristic, quantitative characteristic, attribute,variables (discrete and continuous), nominal scale and ordinal scale.
  • Unit 2 : Organization of data.
    • Statistical enquiry and its stages. Primary and Secondary data. Methods of collection of primary data, with merits and demerits. Essentials of a good questionnaire. Questionnaire and schedule with respect to their relative merits and demerits. Sources of secondary data. Census Enumeration and Sample Survey with respect to their relative merits and demerits. Pilot survey. Sampling – Methods of sampling
  • Unit 3 : Classification and Tabulation
    • Classification- ntroduction, Meaning and objectives. Types with examples. Frequency distributions- Discrete and Continuous variable, Rules of classification. Formation of univariate and bi-variate frequency distributions. Tabulation: Meaning, Parts of a table, Rules of tabulation, Types of tables and drafting of tables
  • Unit 4 : Diagrammatic and Graphical representation of data
    • Diagrams- Meaning, needs, general rules of construction and types. Graphs-construction and types Comparison of tables and diagrams, difference between diagrams and graphs.
  • Unit 5 : Analysis of univariate data.
    • Measures of central tendency – Meaning, objectives, types of averages-definitions, formulae and problems on ungrouped and grouped data. Measures of position- Meaning, definitions of quartiles, deciles and percentiles. Problem on ungrouped and grouped data. Measures of dispersion- Meaning and objectives. Types – absolute and relative measures and their definitions, formulae and problems on ungrouped and grouped data.
    • Moments -Meaning, definition of central moments,description of first four central moments. Formulae for β1, γ1, β2 and γ2.  Skewness- Definition, types with diagram, measures of skewness. Kurtosis- Definition, explanation of kurtosis with diagram, measure of kurtosis based on moments
  • Unit 6 : Analysis of bivariate data.
    • Correlation-types, methods of computationgraphical and numerical methods and properties. Regression-definition, regression equations, properties of regression lines and regression coefficients and related problems.
  • Unit 7 : Association of attributes.
    • Introduction, definition, notations- meaning and methods of association. Yule’s coefficient of association and its applications
  • Unit 8 : Interpolation and Extrapolation 
    • Meaning and utilities of interpolation and extrapolation. Binomial expansion method of interpolation and Extrapolation. Merits and demerits, applications.
  • Unit 9 : Theory of Probability
    • Introduction, definitions-Deterministic experiment, Random experiment, Sample space, types of events with examples. Meaning and definitions of Classical, Empirical and Axiomatic approaches. P(∅) = 0, P(S) = 1, 0 ≤ P(A) ≤ 1, P(A)+P(A′) = 1, Statement and proofs of addition and multiplication theorems and applications.
  • Unit 10 : Random Variable and Mathematical expectation of a discrete random variable
    • Definition and types of random variable. Definition of probability mass function and probability densities function. Bivariate and marginal probability distributions, definitions with examples. Definition of mean, variance and standard deviation of a discrete random variable. Related functions defined on a discrete random variable and applications Statement and proofs of addition and multiplication theorem of Expectation. Covariance and correlation coefficient of bivariate random variables
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