Tripura Board Class 12th Statistics Syllabus
SYLLABUS
SUBJECT : STATISTICS
(Class – XII)
Statistics
Total Page – 04
COURSE STRUCTURE
CLASS XII (Theory)
One Paper Time: 3 Hours Marks: 70
Unit Title Marks
I Mathematics 15
II Correlation & Regression 10
III Probability & Probability Distributions 20
IV Sampling, Estimation & Testing of Hypothesis 20
V Population Studies 5
Total 70
Unit I: Mathematics
Basis concept of Limit, Continuity, and Differentiability. First and second order derivates of a variety of non-trigonometric univariate functions. Maximum and minimum of a variety of non-trigonometric univariate functions.
Integration of a variety of non-trigonometric univariate functions by substitution, by partial fractions and by parts. A standard definition of gamma integral and results involving it (without derivations).
Unit II: Correlation & Regression
Bivariate data. Scatter diagram. Correlation and Correlation coefficient. Properties of Correlation coefficient. Rank correlation, Spearman’s rank correlation coefficient (without tie).
The concept of regression. The principle of least squares. Fitting of Regression lines. Important results relating to regression lines.
Unit III: Probability & Probability Distributions
Random experiment, Trial, Sample space, Sample point and different types of events. Definition of Probability: Classical, Statistical & Axiomatic. The theorem on the probability of a union of (two & three) events. Conditional probability, Theorem on conditional probability for two & three events. Independence of events. Bayes’ theorem and its application.
Random variable (discrete and continuous) and its probability distribution. Cumulative distribution function. Probability mass function and Probability density function. Mathematical Expectation.
Uniform (Discrete & Continuous), Bernoulli, Binomial, Poisson, Geometric, Exponential & Normal distributions.
Unit IV: Sampling, Estimation & Testing of Hypothesis
Population & Sample. Parameter & Statistic. Census & Sample Survey. Concepts of probability sampling and random number tables. Concepts of the Sampling distribution of statistic and its Standard Error. Simple random sampling with replacement (SRSWR) and simple random sampling without replacement (SRSWOR).
The concept of point estimation. The requirement of a good estimator: Unbiasedness, Consistency, Efficiency. The elementary concept of MVUE & BLUE.
Statistical tests of Hypothesis – Null and alternative hypotheses. Simple and composite hypotheses, Critical region, Type-I and type-II errors, Level of significance and size of the critical region, Power of a test. Tests of significance related to a single Binomial proportion, Poisson Parameter and two Binomial proportions using large sample approximations. Exact tests of hypotheses under normal set-up for a single mean, equality of two means and single variance. Frequency Chi-square test & goodness of fit.
Unit V: Population Studies
Vital events. Rates and ratios. Measurement of mortality: Crude, Specific and Standardised death rates, Infant mortality rate. Measurement of fertility and Reproduction: Crude birth rate, General, Specific and Total fertility rates, Gross and Net reproduction rates.
Practical
Time: 3 Hours Marks: 30
Evaluation Scheme for Examination Marks
Practical Notebook 5
Viva Voce 5
Experiments (5+5+10) 20
Total 30
Practical Syllabus
Three Experiments to be given in the examination as follows:
1. Scatter Diagram, Correlation coefficient, and Linear Regression.
2. Spearman’s rank correlation coefficient (without the tie).
3. Applications and fitting of Binomial distribution.
4. Applications and fitting of Poisson distribution.
5. Applications of the Normal distribution.
6. Sampling distribution and estimation of population mean and its standard error under SRSWR and SRSWOR.
7. Large sample tests of a single mean, single proportion and difference of two proportions.
8. Pearson’s chi-square test.
9. Exact tests of hypotheses under normal set-up for a single mean, the difference of two means, and single variance.
10. Drawing of the random sample from Uniform and Normal distributions.
11. Calculation of different rates and ratios of fertility, mortality, and measures of reproduction.
Statistics of Class 12
Unitwise Question Types with Marks Distribution
Unit Title MCQ/Objective
1 Mark SA-I
2 Marks SA-II
3 marks LA
5 marks Total
I Mathematics 3 2 1 1 15
II Correlation & Regression – 1 1 1 10
III Probability & Probability Distributions 2 1 2 2 20
IV Sampling, Estimation & Testing of Hypothesis 2 1 2 2 20
V Population Studies 3 1 – – 05
Total no. of Questions 4+6=10 6 6 6
Total 10 12 18 30 70
N.B. :
1. Internal choice: There is no overall choice in the paper. However, there is an internal choice of one question of 5 marks in Unit – I, one question of 3 marks in Unit – II and one question of 5 marks in Unit – II, one question of 3 marks in Unit-III and one question of 5 marks in Unit – III and one question of 5 marks in Unit – IV.
2. In SA-II & LA-types, total allotted marks in each may be subdivided if, necessary.
3. Questions should be set covering each unit.
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