AHSEC 2nd Year Syllabus 2024-25 Statistics

STATISTICS SYLLABUS FOR HIGHER SECONDARY COURSE Objectives : The main objectives of the course are to enable students .. a. to acquire knowledge on basic statistical concepts. b. to acquire the skill of statistical analysis of data from real life situation in a scientific manner. c. to acquire knowledge on the basic aspects of statistical reasoning and drawing conclusions. d. to create an aptitude for Statistics for those students who show a promise for higher studies and cre- ative work in Statistics. e. to develop aptitude for applications of statistical techniques in Biological Sciences, Social Sciences, Education and Psychology. STATISTICS SYLLABUS FOR HIGHER SECONDARY FINAL YEAR COURSE One Paper Three Hours Marks 100 Unitwise Distribution of Marks and Periods : Unit No. Title Marks Periods Unit-I : Calculus of Finite difference 20 45 Unit-2 : Theory of Probability 40 65 Unit-3 : Elementary Theory of Sampling and Test of Significance 25 50 Unit-4 : Sample Survey 15 40 Total 100 200 Unitwise Distribution of Course contents : Unit-1 : Calculus of Finite Difference : Operators A and E. Construction of diagonal Difference tables. Estimation of missing values, Idea of interpretation. Statements and applications of Newtons Forward, Backward and Longranges interpolation formulae. Idea of numerical integration, General quadrature formula. Statement and applications of trapezoidal rule, Simpsons 13 rd rule and Simpsons 3 8 th rule along with the conditions under which they are derived. Unit-2 : Theory of Probability : Basic concepts of Random experiment, Sample point, Sample space and Event occurrence of an event, Union and intersection of events. Complement of an event. Certain and null events. Exhaus- tive, Mutually exclusive and equally likely events. Probability of an event. Classical, Emperical and axiomatic (without introducing idea of measure theory). Unconditional probability, conditional prob- ability, Dependent and independent events. Addition rule of Probability, Generalized Addition rule of Probability (upto three events). Statements and application of multiplication rule of Probabilities.

2 Syllabi for H.S. Final Year Random Variable and Distribution : Random variable; Discrete and continuous distribution of a random variable, p.mJ. and p.d.f., density function. Representation of discret probability distribution. Probability curve of a continu- ous distribution, Mathematical expectation of a random variable. Mathematical expectation of the function of a random variable. Theorems on expectation of the sum and product of random vari- ables - only application (without derivation). Idea of Barnoulli Trials; Binomial distribution; Mathematical form, occurrence of the distribu- tion, Derivation of the distribution, Calculation of Mean and variance. Poission distribution; Math- ematical form, Occurence of the distribution, derivation as a limiting form of Binomial distribution, calculation of mean and variance. Normal distribution, Mathematical form (without proof). Im- portant properties and their applications. Derivation of distribution of standard normal variate and its applications. Unit-3 : Elementary Theory of Sampling and Test of Significance : Sample and Sampling. Random sampling, Parameter and Statistic. Sampling distribution. Unbiased estimate of a parameter. Standard error of sampling mean and sample preparation for random sampling (without Derivation) - simple applications. Statistical hypothesis - Null hypothesis alternative hypothesis, Level of significance. Test (only two tailed test) for a hypothetical population mean on the basis of information supplied by a random sample drawn from a normal having known standard deviation (application only). Students ’t’ test (only two tailed test) for an assumed mean (examples only), Large sample test (only two tailed test) for proportion (examples only). Examples on use of frequency x2 for testing independence of at- tributes in 2×2 table. Unit-4 : Sample Survey : Sample survey and complete enumeration. Basic principles of sample survey, validity of optimiza- tion. Principal steps in a survey, Errors in a survey. Sampling and non sampling errors. Advantage of sample survey over complete enumeration. Simple random sampling with and without replacement - method of selection of SRS making use of Table of random number, Estimation Population mean and total, use of formula - mean and estimated population total. Limitations of SRS. Idea of stratified random sampling. Estimation of population mean (method of allocation not included). Preparation of Questionnaire and schedule. Idea of pilot survey. ***